I will convince you:

The 2 channel 4 ohm measurement of the 3700 is 168 watts, and the 2 channel 4 ohm measurement of the 4700 is 173 watts. These are the numbers from the graphs which are both taken at the point at which distortion starts to sharply rise for both receivers, (~-85db).

The power vs distortion charts (the ones plotting distortion at different frequencies) are basically identical for the two receivers (the 3700's 5khz distortion rise begins at 7 watts, the 4700's 5khz distortion rise, at 7 watts. All other trends align too.

You don't get both an identical current limited peak power output (170w), and a matching distortion curve (5khz @ 7w), unless the amplifiers are the same.

Further evidence: Denon put a full top down view of the 3700's internals on their site, and just a small piece of the 4700's internals - a couple inches of the amp board can be seen in the shot of the transformer. Upon inspection you'll see: the amps have the same layout, same capacitor size/type/make (do I see some Panasonic FM/FC?), same resistors, same variable resistors, and the same unused pins on the corner. I think it may have been a deliberate move to do this - if the 3700's amp looked exactly the same as the 4700s (because it is) and one costs $500 more, who would buy the 4700? Answer: less people would buy the 4700, especially the ones buying it for a better amplifier section.

So you think the amps are different because the 4700 makes 10 more watts into 8 ohms before distortion starts to rise when driving 2 channels?

Those 10 watts come from the 4700 using a different transformer, one with slightly higher voltage taps for the power amp section. The 10 watt into 8 ohm increase implies a 5% higher supply voltage. A more in depth analysis follows - I've simplified it to what's necessary and my teaching ability.

One thing you need to know to follow is: Power (Wattage) is Potential (Voltage) multiplied by Current (Amperage).

Ok:

Increasing the supplied voltage to an amplifier circuit will result in a higher possible output voltage before clipping begins. This higher output voltage results in a higher output power. Caveats: only within voltage limits and if the additional current required is available. And if this current doesn't exceed the current limits implied by the design of the amplifier.

All electronic components have a maximum current handling capacity - the point at which they conduct less well than is required for desired operation. If it's exceeded, parts can get hot or damaged, or cause damage to other components (from heat or their improper operation during overload). Most commonly, associated components will be caused to operate improperly. Exactly how an amplifier is affected by one or more of its components being in an overcurrent situation depends on the overloaded component, its status, and the degree to which it is overloaded. A safe bet, though, is distortion will begin to rise.

If you design a class AB amplifier to provide 114 watts into 8 ohms, the components in its output stage must remain reasonably linear up to an output of at least 6 amps. The average power of a 114 watt sine wave into 8 ohms is 3.75A. Instantaneous current required for this is higher: 5.25A. The "at least 6 amps" comes from adding the current dissipated as heat by the transistor: a result of the transistor's operating voltage requirement: it needs 5-10% more supply voltage than the maximum desired output. A sine wave needs its peak to be 42 volts into an 8 ohm load for the power to be 114 watts.

Choosing to not use parallel transistors (for fidelity's sake), you pick a 100 volt transistor rated for 12 amps continuous, 20 amps peak. It seems like overkill at first, but it gets de-rated. Taking into account its projected operating temperature and supply voltage (60 deg C, 50V), it is capable of 9 amps peak, 6.5 amps continuous. Since you want the thing to actually be able to drive real speakers with the impedance dips they have in the bass/midbass octaves, this transistor's 9 amps juuuust makes the cut. You surround a pair of them with the components to operate them in class AB (one + direction, one -) and linearize their output with feedback (you make the amplifier). You ensure all the high current components and paths supporting them through 9 amps are adequately sized and properly arranged on the board to ensure distortion does not rise prematurely. In doing this, amplifier potential is maximized, cost, minimized.

The power supplies used in class AB AVRs, are almost always unregulated. Unregulated power supplies consist of a transformer, a bridge rectifier, and capacitors. Voltage is determined during design and cannot be adjusted. Output voltage is proportional to the input voltage. Any load on the output causes a voltage drop which is not compensated for. This is "unregulated". The amount of voltage drop is determined by the transformer's power rating and the size of capacitors used for filtering (capacitors turning pulsed DC from the transformer/rectifier into smooth DC for the transistors). The smaller the allowable voltage drop is, the bigger the transformer and capacitors have to be.

A balance must be struck: you need to limit the supply voltage to the transistor (amplifier) so to not de-rate its current capability too much, and you have to limit the amount of voltage drop under load so that it doesn't fall too far, leaving you with inadequate voltage for 9 amps at lower impedances (where hitting 9 amps is possible). Denon did this with the 3700. The tiny bit of extra voltage on the 4700 is effectively, useless.

Anyway, if you want your 3700 to be like the 4700 and have an undetectable 0.34db more headroom in 2 channel mode while driving your imaginary 8 ohm speakers with flat impedances, you can save $500 and get yourself a variable transformer from the internet for $50 and turn it up to 126v. Then it'll be the same as the 4700 and you'll have $450 extra in your pocket. When you're done driving your imaginary ideal speakers 0.34db louder, you can turn the regulator down to 108 volts (Denon designed all of its receivers to work on 108-126 volts). A 108 volt supply will lower your 3700's power consumption to 75 watts from 100 (2160kwh in 10yrs) while avoiding the crap caused by ECO mode (if that crap affects you). If it doesn't affect you, you can still turn it down to 108 volts and power consumption will drop down to 45 watts in eco mode! (instead of 60) This saves 1296kwh in 10yrs.

A 10% reduction and 5% increase in residential power is acceptable for power delivery over the long term. It's accounted for during the design of everything, not just Denon's receivers.

Like a scientist I like to experiment and you get to benefit from knowing my 3700 shuts off at 97 volts. It likely won't cause damage to run your 3700 on a bit less than 108 volts, but power consumption doesn't go down much more under 108, and the thing isn't specifically designed for it, so you might as well just set it to 108, making sure that during peak load times (eg 5-7pm when voltage is lowest) it doesn't fall to below 106.

If you're considering running your 3700 above 126, you need to know that very likely, the further you go above 128 volts, the faster your capacitors will fail. Capacitors are good up to their rated voltage, but above that, the relationship time to failure is exponential. If you give it 150 volts, you could have only hours (possibly less) until the caps leak and/or blow up. 126 only!