We need to bracket being an "old-schooler" from being "experienced." Old-schoolers will tautologically be experienced gamers in most cases, at least in regards to time. But if your RPG experience is limited to early versions of DnD, then in another sense you aren't experienced at all! It's like claiming you are an experienced traveller because you've been going to Wisconsin Dells every summer for 30 years.
By the way, there is nothing wrong with having only played a small subset of RPGs (nor is this something unique to old-schoolers or universal among old schoolers). It just means your RPG experience isn't very broad. Someone who's been gaming for 30 years but has only ever played legacy DnD editions is in this sense less experience than an omnivorous gamer of 10 years who's played DnD, WoD, Savage Worlds, Burning Wheel, Fate, or what have you.
I think while I agree with most of this, being highly experienced GMing one particular game also gives you an advantage when you're GMing a different game. While the mechanics aren't the same, people - and they're who you interact with as much as rules - are. Gaining sufficient confidence to handle a difficult situation in one game would increase the chance that you'll apply that confidence in a different game.