WHAT'S THE DEAL WITH WATTS?

I run 125 wpc on some 93 db B&W 803's and have to use another amp to drive subs. If you are going to have tone controls and plan to use a bit of bass boost, more power might help. otherwise, the actual difference between 80 and 125 watts is pretty moot, maybe a db in sound level. One db is defined as the actual threshold of change in volume we can hear.

Usually, I do not use my subs and probably wouldn't even need them in a normal house that is divided up more. My house is one relatively big room with two bedrooms on the side away from my speakers.

More important than the actual watts is how these watts work, i.e., how big is the power supply. If the power rating on the amp is at 1000 cps, for example, the power supply is probably too small. If the rating is full range, at least 20-20000 cps, it is what you want. 

I also have an Adcom 65 wpc amp that is heavy for what it is, meaning a big transformer.   For a $50 Craigslist amp, it did quite well pushing two pairs of very inefficient B&W DM 14/1400's, and it was loud enough; however, since these speakers mute the sound when an amp clips, the speakers did shut down much sooner than with the amp with twice the power, meaning it could have blown tweeters from clipping the signal, because of too little power. 

Watts is like HP - it tells you nothing about the torque, it will give you a hint how fast (loud) a car can go but thats useless when you listen in the 1 to 5 Watt range at 80 to 90 db. Its about the instant acceleration, how much torque and at what rpm it will be available. Some speakers (heavy cones) need a high damping factor for the bass but the mids and highs will suffer because the most immediate and best sounding amps are pure high current CLASS A with low feedback.

Krell Vanguard

I’m considering acquiring a new (for me) integrated, under $2k, to drive my KEF full range speakers. They are very efficient (93db) , 4ohm and rated for 50 - 200 watts. It seems that a good amp with 80 or 100 watts per channel at 8 ohms will take these speakers to any volume I’d want to experience in my medium sized living room. So what advantage/benefit in sound am I going to get with 150 -200 watts, or more, per channel? Is it worth spending more for extra power that will never really be demanded?

There are several such discussions on Audiogon if you care to search the archives. Use key words like "spl distance" or "watts needed" or "watts required".
One such discussion is here:
https://forum.audiogon.com/discussions/another-wattage-question

like I wrote on the above cited thread, there is a drop off in SPL at your listening chair vs. the actual spec of the speaker.
Your speaker is mediocre efficiency (I agree with Atma-sphere on this).
Do you listen at 1m away from the speaker? Most likely not.
You are most likely seated 3m (~10’) away.
You, in particular, get further dinged because you informed us that your speaker is 4 Ohms & 93dB SPL. Since the industry spec for listing sensitivity is 1W into 8 Ohms & your speaker is 4 Ohms, you would be feeding 2W into your speaker. So, if we normalize your speaker sensitivity to 8 Ohms, it is actually 90dB (I think another member already pointed this out to you).
OR, if this is confusing to you - IOW, I would have to reduce the input power from 2W into 4 Ohms to 1W into 4 Ohms (per industry standards) & then your speaker will measure 90dB/1W into 4 Ohms/1m.

For every doubling of distance the SPL drops by 6dB. So 1m --> 2m, the SPL = 90 - 6 = 84dB.
Then, 2m --> 3m you lose 3dB (didn’t quite double the distance but increased it by 50% only). So, now the SPL at 3m = 81dB.
Add 3dB for stereo listening.
Subtract about 3dB due to damping effects of rugs, furniture, curtains, walls, house plants, etc.
This addition-subtraction is a wash-out so we are still at 81dB SPL at 1W at 3m listening position.
10W: SPL = 91dB
100W: SPL = 101dB
200W: SPL = 104dB
400W: SPL = 107dB

You can see from the calculation above that if you used a high current 100W amp you could achieve a max SPL of 101dB at you listening position. Reasonably recorded rock, definitely well recorded Jazz & Blues can exceed this SPL number & for sure well recorded classical music.
Realistically you want an amp to reproduce atleast 110dB SPL for your (sudden) peaks in your music program to give you the feel of easy-of-delivery, realistic & dynamic playback, etc. For your particular speaker, you can see, you will need some serious watts. Not only watts but you will need high current watts since your speaker is 4 Ohms (& most likely has some very crazy phase angles meaning that the amplifier will be dumping current into an impedance that is most likely lower than 4 Ohms). This will get expensive for you, no doubt. And, this is also what Ralph/Atma-sphere alluded to in his post date 04-25-2016.
So, the answer to your question is: yes! it is worth spending extra $ on a 200W/ch high-current amp....
(I believe that you can never have enough watts for playback! ;-) It's a mistaken notion that those (supposedly) extra watts are not needed....)