Faithful to a fault, and doesn't live up to the potential this could've had. I'm only an hour in, but I'm confident that's an accurate portrayal of the game.
This (with it's DLC) feels more or less like a mish-mash of Tony Hawk Pro Skater 1, 2 and 3 with HD graphics. If they had taken everything from these games and thrown it into one amazing release, it probably would've done better critically. Instead they hand picked certain levels, hand picked certain skaters, lost a good chunk of the original soundtracks (mostly due to licensing issues), ditched the multiplayer found in the originals (local or online), ditched any kind of create-a-skater and called it a day. It doesn't feel like the "complete" collection it could've been. Like a greatest hits collection from a band that doesn't include all of their biggest songs, it's not really a game that needs to be in every THPS fans collection.
Now, that doesn't necessarily mean the game is bad. Lacking graphical options (outside of resolution) and wonky ragdolling aside, it plays exactly like a faithful HD rerelease should. If you loved the games back in the PS1/N64 days, this will absolutely give you the THPS fix you've probably been craving. (If you didn't or have "grown up" since then, it'll probably seem overly simple and dated.) The game was always meant to be simple though. Simple, but completely over the top... it's by no stretch of the imagination a juggernaut in modern physics. You grind things you have no business grinding, you'll jump gaps that would put the Springfield Gorge to shame... but that was the fun of it... and it still is fun. You'll still spend hours collecting SKATE, hidden tapes (DVD's), busting up bells around School II, making your way down the Downhill Jam. Getting high, pro and sick scores. And all the little challenges nested into each level, that you'll have to explore and find... unless, of course, you still remember where everything is.
If you can find it for less than $5 and wouldn't mind a quick nostalgic shot in the arm, I'd definitely say give it a shot. Just know that it's not the "complete collection" that it could've been.