See also: How to play power chords without fretting hand getting tired?
To me it completely goes along with conventional wisdom. The difference is what you are looking at the wisdom for.
Hooking your thumb over the top is a lot more comfortable and keeps you from dropping your wrist.
More importantly, it lets you use your thumb as leverage for bending notes. When you get to higher string gauges and/or compound bends, it helps to have the extra force from the thumb squeezing down while your fingers squeeze up.
I think you'll find most of the great rock guitarist use thumb-over when soloing, and actually are more likely to put their thumbs behind when playing chords that require the index finger on the low E string.
What are the pros and cons in the context of the style of music and soloing shown in the two videos below?
I think the pros I've outlined. One con is most guitarists can't reach the low E string with their third or fourth fingers when their thumb is on top, and the first finger may have very little power when stretched out to reach it. Another con is when you have your wrist up, you can't stretch your fingers as wide to cover as many frets, and there are some "stretch" fingerings that are difficult to impossible with a high wrist and thumb over the top.
How big of an impact will each way make on the ability to play solos like those?
Personally I can't imagine trying to play rock solos with bending without my thumb over - especially with thicker strings and/or larger bends. I pretty much have to play thumb over as much as possible or I have problems with my wrist. Beyond all of that, thumb over is much more comfortable when you wear the guitar as low as they do. If you want to play like the great rock guitarists, it does help to adopt their techniques. This is one I have recommended to every single guitar student I've ever taught.
Is this a case of where the top guys are advanced enough to be allowed to break the rules?
No, it's the opposite. These guys are experienced enough to know that the rule is actually you should have your thumb over the top as much as possible. Jimmy Page, Jimi Hendrix, and Stevie Ray Vaughan all fretted the low E string with their thumbs over the top while playing certain chords (I also do that routinely but I doubt many will be impressed by that fact).