Well, Old School is 1970s D&D. Limited rules, sort of ad hoc systems rather than a common integrated resolution mechanic, lots of rulings instead of rules, and a vague 'old school vibe' where stakes tend to be low, characters aren't expected to live for a whole 'plot,' and there's not much or any influence from eastern culture like anime or samurai.
New School is 2000s D&D. More granularity, an effort to create a 'physics engine' to run reality accurately, rather than just stuff that is easy for gameplay, and a willingness to have more diverse character options, genres, styles, and so on.
At least that's what the basics mean to me.
So you can do a renaissance of each, which mostly would just mean capturing the best parts of that 'school,' but making it work better. In my mind, 5e is a renaissance of the Old School.
"It won't last. Brothers and sisters are natural enemies. Like 5e and the OSR! Or Vampire the Masquerade and the OSR! Or FATE and the OSR! Or the OSR and the OSR! Damn OSR! They ruined the OSR!"
Flip response aside, the OSR's opposite is going to be somewhat nebulous. Because getting consensus on old-school gaming isn't easy. For some its high-lethality, for others its ridiculous monty haul gaming. Some told epic narratives of the rise and fall of kingdoms and others scrubbed around gritty dungeons.
In my experience, plot armor provides no AC bonus for PCs in OSR (at least in principle, to hear grognards speak of it). For that reason I think players bring to such a game a PC (or multiple PCs!) that are little more than character sheets with stats, an equipment list, and maybe an occupation or two-word "personality" description (aka, "alignment" ). Almost the entire development of character happens at the gaming table, solely through surviving/engaging the encounters of the campaign.
Today, I think it's much more likely for new PCs to show up very fleshed-out with a pretty extensive background-- and with that, some expectation of a destiny a bit more meaningful than "Choked to death on yellow mold spores* on level 1, room 27"
Not specifically a system comparison, but general elements make it old school. So to not be old school, there has to be no murder-hobos, no dungeon crawls or hex crawls, no "that entire race/species is always good/evil", combat-lite instead of combat-heavy, real stories and plots.