Time for non-scientific, layman observations that have yielded no ruined equipment for 25 years.
Regarding OVERpowering: For a long time, I operated under the information that your amp should be more powerful than your cabinet rating. Like 2x powerful. This was assuming I wouldnt turn the amp up near 10. Someone smart suggested it and there was no Internet to bash it. I was told "just use your ears" for potential damage. I never had any ill effects but I rarely had to turn up over 5 or 6 for ear bleeding loudness so the speakers never strained.
My recent GK cabinet manual says:
DO NOT connect speakers with a total power handling capacity below the power output rating of your amplifier. If your amplifier is rated at 400 watts at 4 ohms, then the combined power handling of your
speaker enclosures should be 400 watts RMS or higher at 4 ohms.
So, this suggests that you can damage cabs by overpowering but it's silent on underpowering, which implies to me that underpowering isn't a threat to damage stuff.
I defer to just keep things roughly matched up so that 1) the speakers are highly rated enough that you can turn amp up loud enough to get the volume and sound you want and 2) the amp is powerful enough to not have to turn amp so loud that you over-stress the amp (I know nothing of this other than what God- knows- who wrote here). These are layman's observations but I've never ruined an amp or cab, no has my friend who seems to operate the same way.
I use a 500w 8 ohm amp into a 350 rated 210, or a 300 rated 112 or a 600w rated 212. My volume is between 2-6 on any amp and I turn the pre up to just under clipping.
I use the same amp at 800w at 4 ohms into a 300w rated cab paired with a 600w cab (so with 400w going into each, one is overpowered and one is underpowered- this is a potentially dangerous thing to do as the 300 is at risk but I don't turn up past 5 and the speakers still have much room for more).
I also have a 350w/500w amp that I run into the same cab configurations...so as little as 250w going to the 600w. No problems.
So there you have it....a range from 350w underpowered (less than 50% of potential) and 100w overpowered (33% over but never turned up past 6 so not really).
Nobody can seem to agree on this subject (science has been cited to back up opinions on both sides) so experience tells me to just stay in the ball park and use your ears. If you need to turn up to 8-10 to make your 250w amp loud enough to make your 600w speaker sound good, get a bigger amp. If at 6, your 800w amp is pushing your 350 w speakers too hard, get a bigger cabinet or add a cabinet (ideally a matching cab to assure a good sound with no clashing of any sort, according to those who study this).
Thanks.