There are three things that produce SPL and the amp power is only one of those things--without knowing the other two there is no real answer.
The three things that determine SPL are as follows:
1. Speaker efficiency or how much SPL is produced at a specific distance--normally one watt at one meter distance
2. Distance from the speaker
3. Amplifier power without clipping
Speaker efficiency is HUGE and determines if you speaker can even get to reference levels (105dB at your listening position)--some speakers won't no matter how much power you throw at them.
For example--say you have small bookshelf speakers that produce 86 dB one watt/one meter or you stuff some JBL 4722N actual theater speakers in your room. The 4722N is rated at 103dB one watt/one meter. Or, in my case my mains are at 98dB one watt/one meter and they are 8 ohms. Now say you take and SPL reading and one meter from your speaker then take another SPL reading at your listening position and notice it is 10dB less than at one meter. This means the speaker needs to generate 115dB at one meter to produce 105dB at your ears at your seat. This means you need enough gain from the amplifier to get your speakers to produce 115dB at one meter--time to calculate amp gain! Here is what would be required for those three speakers to get you there (there is also power compression but to keep it simple--we will ignore that for now)
86dB efficient speakers 800 watts for +29dB of gain
98dB efficient speakers 50 watts for +17dB of gain
103dB efficient speakers 16 watts for +12dB of gain
In short, if you need 115dB at one meter to reach 105dB at your listening position and your 86dB speakers can only handle say 200 watts--you will never reach reference levels--ever. My 98dB efficient speakers hit reference at 50 watts and the huge JBL theater speakers crank it out easily at 16 watts. Even if the 86dB efficient speakers could handle 800 watts, you'll need a professional PA amp to power them. Meanwhile, the 98dB efficient speakers could run on any 100 watt per channel AVR with room to spare very easily. Heck, the JBLs could run on chip or tube amps as they require so little power.
The second factor is distance from your speakers--huge difference between 2 or 3 meters (6.5 to 10 feet) and 6 to 8 meters (20 to 26 feet) Another factor related to distance is how large is the room or if you are doing HT outside for some summer movie on the lawn fun. Enclosed rooms don't have the drop off in SPL as drastic as being outside, not a factor generally in consumer audio as it is more a professional audio concern. Say you are at 6 meters or 20 feet in a large basement, it generally (real world) takes around three times the power than 10 feet (you lose around 4.5 dB as the distance doubles in most enclosed spaces which demands about three times the amp power) Outside it can reach 6dB loss as the distance doubles so you require four times the power at 20 feet than you did at 10 feet.
A word on power compression, all speakers suffer from it and some professional speakers and drivers quote power compression in the specifications. Generally speaking, for professional drivers when run at their RMS value limits--power compression can be in the range of -1 to -3dB. Some of the spec sheets will tell you the power compression at 1/3rd power and so on. Say you have a speaker that has -2dB of compression at the RMS rating, then subtract that -2dB from the maximum output. For example, if you have a speaker that will meet your SPL requirements at 200 watts but it will compress -2dB from voice coil heating, non-linearity of the suspension etc.--you would need to add +2dB of amp gain or push 320 watts instead of 200 watts.
To simplify things a bit, if you have a KNOWN amount of power you need to get the SPL levels correct at your seated position--say you use efficient speakers and sit rather close so 50 watts is required and your speakers are 8 ohms--any decent AVR will do that all day long without ever clipping, overheating or shutting down. It don't matter if you use an AVR, a 500 watt per channel gaint home amp or a commercial amplifier used in stadiums that punch 10,000 watts per channel into 2 ohms--50 watts is 50 watts as long as the impedance of the speaker remains in spec for the amplifier.
Now if you use an AVR with 86dB speakers and listen to them at 4 meters (13+ feet) and expect clean and clear sound approaching reference--it won't happen. Throwing more power at them be it 200 watts or whatever will help but you have a long way to go to get there. For that reason, if you want reference levels beyond 10 feet--it is best to use speakers of higher efficiency to start. To get a speaker to increase 10dB so it sounds twice as loud requires 10 times the amplifier power--so if your speakers are 10dB more efficient to start, that cuts out 90% of the amp power required.
Back in the day, I had a pair of speakers I really enjoyed the sound quality of--they were rated at 87dB one watt/one meter. Attempted to go to "rock star mode" with them and blew the woofers out twice. To prevent that, I used a speaker switcher for the lower efficiency speakers when sound quality was of utomost importance--then had "speaker B" as a pair of 3-way PA speakers that punched 100dB one watt/one meter for party mode.
The PA speakers required 20 times less power to provide the same SPL as my lower efficiency speakers. My main speakers would need 100 watts at XXX SPL while the PA speakers required only 5 watts to do the same thing. After that, I would select the correct speaker for the job and never blew another speaker driver in my lower efficiency speakers--bonus!
These days I have very efficient speakers that are a solid 8 ohms stable--I have no need for more than 40 watts to go to them (or less) to reach reference levels. Now if your speakers have a very low impedance dip--say down to 2.5 ohm and such things, then you'll need a high current amplifier to work properly. A buddy of mine had a pair of Kappa 9 speakers from the 80's, they would dip down to 0.8 ohms at one point in the operation although they were rated "4 ohms". His Marantz integrated amp would run hot then shut down in protection mode because of the very low impedance of below 1 ohm. He had to get a 75 pound amp of huge just to drive those speakers--and that big amp would get toasty. That is a special case but some people will take 4 ohm speakers that drop down to 2 ohms in the passband and connect them to a basic AVR or integrated amp and they will shut down. It is not a problem of the AVR or integrated amp, it is a fault of the speaker design/crossover network in the speakers that demand insane current from the amplifiers. This is why you need to get an impedance sweep from 20 Hz to 20 KHz to determine the load placed on the amplifier and get an amp that is rated to do that. If you have an 8 ohm speaker that does not drop below 6 ohms anywhere in the passband--you are good and any AVR will easily drive them without overheating or kicking in the overcurrent protection devices.
In summation, as long as you use reasonably made amplifiers and use them within their operating ranges without clipping or overloading the amplifier--it won't matter. However, if you need more power to get to the SPL you desire than either the AVR, integrated amp or amplifier can provide--that matters! The term for that is "Not enough rig for the gig" and I've been there! My very efficient main speakers sound great if they run on my 100 WPC AVR, my 120 WPC studio amp or my 400 watt per channel PA amp--all screaming along at those rare 40 watt peaks into 8 ohms. My AVR runs nice and cool, no clipping issues and provides more power than I can use in my living room so it is the right choice. My studio amp I use in the garage to drive PA speakers and my PA amp is used to drive subwoofers but I can swap them around for entertainment when the mood strikes.
Hope my endless jibber-jabber cleared things up a bit for you---big difference between needing 16 to 50 watts and demanding 800 watts to hit your required SPL. One last thing to know, the more watts you drive a speaker with--the more distortion the speaker generates (the more movement the more distortion) This is why pro sound speakers use such large drivers in huge boxes and horns etc...to minimize movement of the drivers and lower distortion while getting maximum efficiency and power handling. All part of the game, just remember speaker efficiency, distance and dB of gain required for your amplifier needs. Enjoy!