help me decide

Here's an opinion for ya: Keep the old Denon AVR, and put your whole budget into speakers.

OK, but then follow the same logic: Go with one of the AVRs and put most of your budget into speakers.

Well, then it's a good thing you found AVS!

The basic advantages of an AVR for two-channel systems are:

1) They are generally more cost-effective—you get more power for your dollar, leaving more money for speakers, which have a much, much greater impact on the overall quality of your system.

2) Most now include some form of room correction, which can at least partially offset any problems in your listening room (and all listening rooms have problems). After speakers, your room has the greatest impact on the sound quality that reaches your ears, far more than any other component. Stereo amps cannot do this.

3) If you want to add a subwoofer (which you should consider), AVRs offer bass management, which easily integrates your sub with your speakers.

In terms of overall sound quality, there's a substantial body of scientific evidence that, assuming they're powerful enough for your speakers, audible differences between amps are rare to nonexistent. AVRs, because they're designed to drive 5-7 speakers, generally provide plenty of power when driving only two. And thanks to room correction, AVRs can actually be made to sound better than stereo amplifiers.

That's an old school answer.
The AVR's advantages for the listener to stereo recordings are:

(1) Equal sound quality for 2 channels and the same power rating
(2) Bass management for optimizing use with subwoofer
(3) Digital inputs
(4) Center channel output
(5) Most now have automated system tuning facilities including supplied measurement mic

The desirability of an upgrade path including a subwoofer is illustrated by the following estimates of maximum undistorted SPL versus frequency for a SOTA 5 inch driver in an unvented box (Linkwitz). I would expect no more than 3 dB more from a vented box (YMMV)

Hz Max SPL
20 76
30 83
40 88
60 95
70 97
80 100
90 102
100 104
130 108

I would hope that any speaker for critical listening would be capable of undistorted operation at no less than about (+/- 3 dB) 100 dB SPL.

Therefore a conservative view would be that a speaker with a single 5 inch driver would be capable of low distortion operation down to 80 Hz. Being pretty optimistic about driver quality, modern speakers based on 5" drivers need to be augmented by subwoofers for use by critical listeners.

IMHO, the Denon 2113CI would be a good choice. You'll get Audyssey MultEQ XT room correction software, networking, and extra year warranty.

Only if the speakers you choose require well over 100 wpc to operate.

Then why are you asking about a power amp?

And how many of them understand how an audio system and its component parts work?

A power amp adds power. That is all. It takes an electrical signal, and makes it a stronger electrical signal. (Granted, any amp distorts that signal a little. But the distortion caused by the amp in even a basic AVR falls well below the level that would make it audible. This is part of what the folks you googled don't understand about audio.)
A key virtue of AVRs is that they do all the things you need done, unlike most two-channel gear.
This is more evidence that you've been listening to folks who don't understand how an audio system and its component parts work. "Separating" the various component parts of an audio system offers no inherent advantages. (And remember, they're still connected. It's just that the wire is a little longer!)

This gets us into the "If science was up for a vote" argument. There is a whole raft of false beliefs on the web that I've been known to call "Audiophile Myths". There is no actual science behind them. For example, component break-in. For example, expensive wires and cables sound better. For example, Integrated amps always sound better than receivers.

My opening shot would be that a lot of Integrated amps are pretty much receivers with stuff pulled out of them. This makes the rest of the discussion easier because all we have to do is look at the items that are pulled out, and see if they help or hurt sound quality.

So, what do you pull out of an AVR to make it into an integrated amp?

(1) I'd take 3-7 power amp modules out of my AVR to turn it into an integrated amp.
(2) I'd take out the AM/FM second out of my AVR to turn it into an integrated amp.
(3) I''d take the digital inputs and the surround decoders out of my AVR to turn it into an integrated amp.
(4) I'd take bass management out of my AVR to turn it into an integrated amp.
(5) I'd take the system optimization system (Audyssey, YPAO or MCACC) out of my AVR to turn it into an integrated amp.

(1) Taking the "extra" power amp modules out won't help SQ because if I run my AVR as a 2-channel device they are taken out of and away from the signal path by the configuration circuits, If they receive no signal, they use hardly any power at all.
(2) The AM/FM circuitry is tiny, uses no power, is well shielded from the rest of the AVR and again draws very litle power whether its on or off,.
(3) The digital signal processing is done by a DSP. Its programming is precise so when functions aren't needed they have no effect on the signal purity. The analog signal flow is the same regardless. The converters are as clean if not cleaner than the power amps so they have minimal effect on signal quality.
(4) Bass management is handled by the DSP so the same consideration apply to it as (3).
(5) System optimiation is handled by the DSP so the same consideration apply to it as (3).

Bottom line, the stuff you would take out has no effect on sound quality other than to provide its defined functions, when you need it.

That is false.

The only reason to add a power amp to an AVR is if the AVR's power amps lack the power. Because it takes a ton of power to provide extra loudness (10 times the power to go twice as loud) any power amp you add has to be rated at 1 Killowatt or more to have a significant audible benefit.

Another factor is that many AVRs no longer provide preouts needed for proper audio decoding and DSP prior to sending the signal to an external amp. I know denon in my model year only provided preouts from the 3311ci and up. I'd find it hard to believe you'd need more than 100 wpc. If so, you might be better served just walking up the chain to a higher power AVR. They go to about 150 wpc, but I don't know that you need to.

I have speakers that could take more power than my 3311ci puts out at 125 wpc in my 2 channel setup, but to be honest, I can get insanely loud listening levels with it, and don't see the need for more power although the speakers could take quite a bit more (supercharged songtowers).

I thought you were talking about the AVR.

Per the ATSC standard, TV's need only handle MPEG-2 video and AC-3 sound. AFAIK that is typically all that they actually do.

http://eeweb.poly.edu/~yao/EE4414/spectrum_HDTV_review.pdf

I understand that there may be a recent update related to adding support for AAC sound.

It is AVR's and Blu Ray players that have the support for so many different audio and video formats.

http://www.blu-ray.com/faq/