The difference between these two amplifiers (the amplifier portion of the receiver) is so insignificant that for intents and purposes they are the same. To the difference into proper perspective, power numbers need to be expressed in decibels, and if the simple calculation is done correctly, the number can be regarded as the decibel value for the difference in sound pressure. The 80 Watt amp is +1.25 dB relative to the 60 Watt amp. This is so small as to be almost within the margin of error, and it is smaller than the difference in perceived sound volume for connecting two different sets of speakers where one of them is 1.25 dB more sensitive than the other. Two different sets of speakers chosen at random will likely differ in sensitivity by at least dB. Note also that in the specs for the two receivers, the distortion rating is identical for both, and taken under identical circumstances for both. For intents and purposes the two amplifiers are identical, and they may well be identical despite the quoted max power being very slightly greater for one vs. the other. Most likely the power supplies are identical, and most likely the +/- DC voltage supplied to the amplifier is the same for both, and most likely everything else in the amplifier is the same for both. I would assume they are the same unless and until someone does a teardown and finds something different, or measures the DC voltage coming out of the power supply and finds them to be different. It is most likely that the extremely minor difference in quoted power rating is the handiwork of product managers and/or marketing, which deemed it essential for there to be a slight difference in power rating, commensurate with the difference in MSRP.
While it is possible that there is a difference in the sensitivity of the two volume controls, I think this is not especially likely. Not saying that it isn't true, only that if it is, I would be a little bit surprised and would say, "Huh."
I like this present line of stereo audio integrated amps by Yamaha. I especially like the variable loudness control. Assuming this control does what it should do, the amount of low-frequency and high-frequency emphasis will vary according to the position of the main volume control, such that the perceived tonal balance should be much the same regardless of whether you are playing it loud or quiet. This is a very practical feature to have in a received, and in my individual opinion the loudness control is a significant advantage of receivers with this control compared to receivers without this control. Loudness controls sort of fell out of favor back in the '80s, and I'm glad to see that Yamaha has brought it back. I also like the aesthetics of these receivers. And very affordable. A lot for the money. If you consider inflation, a receiver that cost about $50 back in the mid '70s would probably cost this much or more today, and you could not buy a half-decent receiver for $50 back then. It seems remarkable that it is possible to buy a receiver like this for this little money.
Congratulations! You made a very wise purchase!