Eh, I don't know. I think the fact that there's still Batman '89 interest and awareness says, to me, that it does hold up. Dated, yes, but it certainly doesn't fall apart. I mean, it's constantly pitted against The Dark Knight (thankfully that hasn't been the case lately) with literally thousands of polls, that's got to mean something. The fact that it's quality is even questioned to this day should be an eye opener. It didn't just get lost in the shuffle, forgotten like the 80s Punisher (or the new one for that matter) or the 1990s Captain America. It transcended, became a household name and franchise.
The Original Star Wars trilogy and the early Reeve Superman films look hokey, dated and weak to today's standards but they're still classics.
It's the mindset you have going into any particular film. If you're not willing to suspend your disbelief and only see said film as "old" then you won't let yourself enjoy it. If you purposely look to out a movie and find flaws in it then you'll find them. It's also worth noting that you'll find them in ANY movie. However, if you just enjoy it for what it is and look for good then age doesn't matter and you will find something to enjoy. This applies to any age group as well. If you let yourself accept it and you see the quality, then you will.
If you go in putting a wall up, then you won't.
Of course these older films wouldn't fare if they were made today, they set the record for what was/is great. Every movie, I don't care what it is, is "of it's time". It never makes sense to me when people contemplate "what ifs". Batman came out in 1989, that's it. There are no what ifs. It set the standard for comic book films, at that time and while it may seem shallow and light now, looking back it certainly wasn't when it was released. People took that ____ seriously because it hadn't been done before. Now, it's been taken for granted and evolved, that's where The Dark Knight comes in. It's a progression, film and ideas evolve.