Classes that become weaker:
Pyro because the skill ceiling is limited, flame range is easy to avoid and most classes are good against pyros provided they can hit their shots.
Knife spy due to increased awareness of most players and less exclusive reliance on the pyro for spychecking
Heavy because better teams are better at focusing and turn you into the sitting duck you really are.
Classes that become stronger:
Snipers will consistently hit the easy shots and have a very good chance of hitting the hard ones so you can't just juke and weave and hope you don't get hit. Either you stay out of sightlines until a flank class or spy can kill the sniper or that guy can easily destroy your push. Sniper is probably the second most important class after demo in high level HL.
Scouts and soldiers in high level have better DM so they can be much more menacing, especially from the point of view of stuff like engies and pyros, who can probably have a good chance of winning 1v1s against these classes in lower levels but against the best DMers will simply be annihilated.
Amby god spies (see most EU Prem players) are almost as good as having a second sniper and can usually get safe picks where a backstab would most likely be denied. Very dangerous to play against and require focus from your flank classes since they'll probably stay far away from the pyro.
Medic becomes more important because often in lower levels the better DMers win and are able to win teamfights even with worse heals. At higher levels everyone is pretty good at DM and better at capitalizing on a medic pick, or several lit players.
Classes that have more or less the same importance
Engie will always be a key part of your defence, and minisentries never stop being good at denying the flank. Plus high level engies usually have the shotgun DM to match scout mains and be effective on the flank.
Demo is the most important damage class no matter what level you're on