He's effectively immortal. Selene can only incap him for a win and it takes a loooooot to incap Klaus unless you use one of his weaknesses which Selene doesn't have.
As for speed, it's probably equal. Both can blitz bullet timers easily though Klaus has better travel speed which could be a small advantage.
In terms of strength, not buying that Selene is stronger. The van feat is impressive but that's probably around 5000lbs of force ahe redirected, they're probably equal there.
And then there's Klaus being a werewolf which further amps him, nevermind that his bite might be lethal.
For this fight, she only needs to incapacitate him to win. Klaus's neck just has to be broken to achieve this, besides selene's bullets dstroys lycan heads, which are bigger than Klaus's she'd shoot his head to shreds, the argument that nothing can kill him except white oak is a NLF. We only take things he has survived, any other thing is just conjecture. People in TVD just have no creativity. I remember some foolish demon telling buffy the same thing about being unkill-able according to all books, you should see how creatively she tested the theory out. Selene has more than enough power to break his neck.
As for speed, I still don't see any bullet timing feat. Despite me proving that according to the plot of the show Originals are not able to dodge bullets. The thing with travel speed combat speed is Combat speed and reaction is almost always higher than travel speed, AFAIK only reason travel speed may be faster than combat speed is if a special method is employed to achieve the speed that cannot be applied in battle. So why would the TVD have outrageous travel speed but limited combat speed.
You're joking on the strength feat right?? Mate, she flipped a moving van that weighed a few tons off the ground and across a room without any strain, you compare that to elijah lifting the side of an rv?? Mate I already mentioned how it was much much easier to lift the side of something compared to the entire weight. Marcus in evolution hit the side of a truck and forced it to slam against a hill, and pulled down a helicopter. Constant strength feat placing them above TVD in strength. You claim Klaus is stronger?? show me feats backing this up.
Further amps him to what level?? We don't see any noticeable difference, sure it makes him stronger, but by how much. Elijah can still always give him a fight. So even if he is stronger, it's clearly not by a huge amount. Yeah, werewolf bite does nothing to selene.