Both because they aren't even similar other then both using skateboards.
THPS is an arcade game. Skate is a skating simulator, will except 3 that's a "how bad can you crash bro?" simulator, but they are different games for different things.
I love both.
Couldn't agree more with this post. They are about as diverse as two games can be whilst still being considered the same genre, as different as Rocket League and FIFA.
Skating was my life in my teens (early 90s). Sadly too many busted ankles/wrists and friends moving on from it means I no longer skate, though I still follow the culture heavily.
THPS was my jam, played the shit out of that series, but the fun really lies in the high score/crazy lines/collectibles nature of the game. Once I was done with the objectives, the fun of actually skating around wears off pretty fast.
The Skate demo was an absolute gamechanger. The most time I've ever put into a demo by a country mile. They
nailed the feeling of actual skateboarding, with a pretty much perfect control scheme. Objectives and scores aren't really necessary for me. The beauty comes from being given an open world playground for you to do what you want. I've still 100% all three Skate games, but I've put way more time into HUDless freeskate, just skating around expressing myself like I did back in my teens. I'd actually be interested if any skater/snowboarder/wakeboarder etc prefers THPS over Skate, as they nailed the feeling so well that unless you know what it feels like it's hard to appreciate.
So it's Skate by a vast, vast amount (specifically Skate 2 - getting off your board was sorely needed, and it has the dam drop-in insanity). The one nagging flaw in all three was how they treated lip tricks on transition - you couldn't ride smoothly out of a grind or slide, you had to ollie back into the ramp, killing the flow.