I think that great ES-335's are easier to find.
But very good Les Paul's, standards and customs, are generally very good guitars for what's out there too, especially after you plug them in and turn them up. A big set of good humbucker's like the 57's or 490's are going to sound good no matter what.
Playability may vary and again I'd give the nod to the ES-335, but Les Paul's are not hard to tinker with and you can usually dial them close to where you can live with the action. You want to be sure that there are no issues with the neck, so it should play well mostly right from the start.
Neck size and profile is important and something you just have to try out and know what you are going after.
The thing I find with 335s is they vary a lot in character, so in my experience when people talk about a 'good' 335 being hard to find they have a fixed idea in their head of what a 335 should sound like and discount anything outside of that window.
For me though there's at least three families within 335: the ones that sound like archtops with a little more smoothness of attack and longer sustain (your ideal 335 for prominently clean sounds), the ones that are more raunchy and punchier (the classic blues rock 335s) and the ones that behave more like Les Pauls with a slightly looser low end (the best for indie and higher gain). Personally I like all three varieties, I think it's one of the cool things I like about 335s that they vary so much, but I can see how someone who has a preference for one of those varieties might find a lot of 335s lacking.
It’s easier to find a consistent LP in tone . Like has been said , 335s vary a bit . It’s easier finding a stellar 335 in regards to QC than a LP . Mostly because they crank out a lot more Lester’s than 335s .
If buying new they are both easy to find. If buying used...they are both easy to find. I’ve played over 50 Gibson guitars in the past 15mo and all but 2 were great guitars. Half of them were exceptional guitars. People over think this stuff too much.
As a Canadian, right now I can confidently say both are very hard to find new, especially if you don’t live in or close to one of our major cities. There aren’t any new Gibson USA 335s in stock right now through our country’s biggest Gibson distributor. If you want a VOS Historic Reissue 335 for $7,399 (LOL!), there are less than a handful in stock across the entire country. Hard to “run the racks” for a good one when there’s nothing in the racks beyond a few extremely overpriced CS models. A few stores have LPs in stock, mostly Studios and Classics, but Standards are increasingly hard to find and there aren’t any in stock online either. Some smaller stores may still have a few new Gibsons in stock, but it’s pretty sad when the only thing your equivalent of Guitar Center has to offer (at the very start of their annual Gibson promotion month, no less!) is this:
With respect I never fully understand these questions...if this theoretical "just okay" LP or 335 that most of us must own is picked up by Tom Bukovac, and he absolutely smokes us on it and sounds just like Tom Bukovac, does that still mean it's a "meh" guitar? I can't imagine there's a universal measuring stick for what makes a "great" example.
There are way more variations on Les Pauls, across a much, much wider price range than 335s. I feel like I could take any 335 off a rack and go straight to a gig with it. Not the same for LPs, and I do love them both