The difference between the two is the 600C uses a pair of passive radiators to increase output. They are both 3-way WT/MW designs, and have fairly flat frequency response if that matters a lot to you.
It seems to me that Paradigm and Klipsch put the most effort into centre speakers than the vast majority of other companies. The only way to tell if it's a better centre than the 440C is to audition it in your home, in your room, with your electronics and sources material. IMHO, whill there may be a bit more "fullness" to the sound sue to the larger woofers, clarity MIGHT be improved a bit, but you probably won't be improving on the dynamics of the Klipsch.
Again, what are your mains, sub, AVR, speaker settings, crossovers, subs, etc? Knowing this info can help us make better recommendations. You wanted a CLEARLY better centre; well, you will have to go bigger to get "better". If Klipsch, the RP-600C, RP-504C, or RC-64iii (in increasing order) are the "better" centres. To increase performance further, you would probably have to go to a completely different configuration (Ascend Acoustics Sierra Horizon with RAAL), speakers in a higher class than your current ones (Paradigm Prestige, Revel, Kef R-series, etc), or Pro Audio-derived speakers like the MTM-210C or JTR Noesis monsters.
Thanks! (I see someone asked a question, but your reply was helpful to me as well- the OP).
Ordinarily I would suggest the Infinity Reference RC263 - especially when on sale - as it would probably be the closest match to your mains. Unfortunately, your "sub" isn't really a "dynamo". You are likely getting the same bass extension as your towers from it.
Maybe your issue is a sound mis-match between your fronts and centre. Some people don't notice any difference, while others find it quite distracting. The ability to level-match the SPL output at the MLP is one thing that AVRs do extremely well. Until now, I had never heard of a Sherwood AVR with Trinnov processing. Perhaps a more modern AVR, even one off of Craiglist, will help make a difference. You could certainly purchase one to test it out and return it if not happy.
Another thing to think about is a "proper" subwoofer. As I said above, the ML one is not likely doing anything in your room. I suggest a high-output, ported 12" sub from (in ascending order) SVS, Monoprice, Hsu, Rythmik, or Outlaw. The ability to play clean, flat, accurate bass from the crossover frequency (usually 80Hz for bass management and 120Hz for LFE) to below 20Hz is literally eye-opening. This will allow your speakers to play louder and with more clarity without the need to play the deep notes.
Thanks for the feedback!
While the built in subs on my front towers are very nice and the ML is not the loudest / largest sub by any stretch of the imagination, I can assure you the ML sub is definitely helping a lot with the overall experience. I prefer it to my prior 15" sub which died on me (amp failed, but I still have it).
I auditioned the ML first since the woofer driver is "only" 10" and I wanted to be sure it met my needs. I was very happy during the audition and was not disappointed when I hooked it up at home to say the least. Low frequency effect (including explosions) in sound tracks are more than loud enough with no distortion and literally rock the room, even though the HT is set up in a very large finished basement. Frankly anything larger / more powerful would be overkill for my needs and I already worry about my ears during loud scenes as it is.
Regarding a new center, I am not unhappy with my system at all. However, I just figured that now that I have my 77" OLED and Hi Res Audio / 4K Blu Ray player (which I use to pass 4K video to the TV via 2nd HDMI output on the BD player given receiver is not 4K capable) that I might want to explore a new center to see if I could benefit from a better center (e.g. ideally one with dual 6 1/2" woofers and 3-way design). The RP-440C woofers (while there are 4, are only 4") are the main 'downside' IMO.
That being said, my RP-440C is a very nice center and maybe I am expecting too much from a THX-365C or C2+ although at least one here said they expect it would be a noticeable upgrade.

If so I may hold off.
At least I am not too concerned about the potential new centers both being 4 Ohms, based on your comments and those of Zorba that it probably won't be an issue.
The unless you play it very loud caveat it there however. I hence readily admit that I am always careful to keep things within spec and would prefer not to have to even worry about any potential accidental amp damage - For instance I was scrolling surround sound modes for Hulu non-5.1 content this weekend and one mode was literally twice as loud as all the others. Luckily I was by the receiver and quickly turned the volume down by hand to avoid any damage. With a 4 amp center it might have been more scary than with my current RP-440C.
Also if I ever want to crank it up or if I even inadvertently do so (albeit unlikely), I do not want to have to worry... My system is currently worry-free. The Klipsch is easy to drive to very loud levels thanks no doubt due to its high sensitivity, being 8 Ohms and the heavy duty amp section in my receiver

(* It was a surround sound mode I never use but was using an optical output from TV to receiver to test HBO Max free trial that came with my Sony BD player - the Sony 800M2 does not have HBO Max app (not a concern since Netflix and Prime are my main concerns; Hulu is the other one; it is not supported by the BD player but I use the app on my TV for that).
I may bite the bullet on the C2+ or THX-365C and give it a shot anyway (despite the 4 Ohm impedance) and try to be more careful than usual even.
At the time I bought the R-972 AVR, it was based on build quality, performance and also to get HDMI, Dolby True HD, dts Master HD and was further convinced by the professional reviews which called out the "sought after Trinnov room correction system" (same as the one that came with the $13,000 professional system at the time). I also got a great deal on it, which I am still amazed by.
While I am considering a 9.2 receiver (not 7.2) for either now or later in the year, mostly to get 5.1.4 Atmos capability (e.g. Marantz SR6014, SR7013, Denon 4500H etc.), and while I am at it would get HDMI 2.x and eARC etc. of course, I am not necessarily in a rush for a new AVR - Aside from Atmos and dts X support, I have the features I need most (lack of eARC is not a huge deal to me yet). Also not sure how much Atmos will improve my system since I have no options for in-ceiling speakers in my large HT media area.
The R972 has been rock solid (reviews below) and I use my Sony UBP-X800M2 for 4K output to the TV. So aside from lack of Atmos and ARC/eARC, my AVR has what I want, especially sonically.
That being said I am checking deals for 9.2 receivers (going to jump over 7.2 straight to 9.2 so I can get 5.1.4 Atmos without an external amp).
In case it helps, below are some professional reviews of the R-972. These are admittedly from 2010, but aside from not having Atmos, dts X and HDMI 2.x [and 4K for which I have an easy workaround using the UBP-X800M2], it is an amazing AVR and I know that I would need to get a top of the line current AVR to give me the audio performance, build quality and effortless power.
The Sherwood Newcastle R-972 A/V Receiver is the latest high-end receiver in the Sherwood product lineup. The Newcastle brand is Sherwood’s premier product line. The R-972 A/V receiver boasts some impressive features including 7 channels of amplification at 100 watts per channel, 4 HDMI 1.3...
hometheaterhifi.com
Price: $1,800 At A Glance: First A/V receiver to include Trinnov Optimizer • HQV Reon-VX video processor • Big beefy chassis Say Hi to Trinnov The Sherwood Newcastle R-972 A/V receiver is the first to include a new player in auto setup and room correction technology. Say hello to the Trinnov...
www.soundandvision.com
One of the most exciting new technologies exhibited at this year's SOTU event was a live demonstration of the upcoming Sherwood Newcastle R-972 receiver featuring a built in Trinnov Optimizer room EQ
www.audioholics.com
An audio/video receiver in Stereophile? Heresy!
www.stereophile.com
THE SHERWOOD NEWCASTLE R-972 WITH TRINNOV OPTIMIZER Is this the most advanced A/V receiver on the planet? Thanks to its Trinnov Optimizer Room Correction system, the Sherwood Newcastle R-972 just may be. This flagship receiver in the high-performance Sherwood Newcastle line-up, winner of...
www.avsforum.com
Speaking of 9.2 receivers, since I am researching those too now: While I would ideally like a Marantz SR6014, SR7013, Denon X4500H or better, I wonder whether a 9.2 Atmos THX Select Onkyo NR-7
97 (someone has a nice deal on one and I could get one now rather than wait given all the recent spending) be a downgrade, purely speaking in terms of amplifier and overall sonic performance compared to my R-972 Trinnov?
I suspect I am probably better off waiting / getting one of the other 3 receivers noted above (or better of course) to avoid being disappointed...
Also heard about Onkyo reliability potentially not being what it once was unfortunately (my first quality receiver, before surround sound was an Integra TX-890 - 360W per channel at 2 Ohms. The good old days.
The 40+lbs Trinnov never feels strained or even gets hot thanks to the large heat sinks etc. My HTR before that was a 62 lb beast - Elite 47TX THX Ultra 2 (still have it - will sell it eventually after COVID concerns are out of the way) which I replaced with the R-972 to get HDMI, along with Dolby True HD and dts Master Audio etc.
So I do not want to take a step down in overall sound or build quality.
Wow, this became a novel!!!
Anyway, thanks again! Appreciate the feedback / insights / recommendations. Now to determine if this is a case of upgradeitis or not. 