Definitely a weird one, there's the argument that because Arsenal create many more chances than Leicester, Vardy will thrive on them but I'm not sure if Vardy will fit their style of play any better than what Giroud or Welbeck do. Vardy needs space, it's why he and Leicester were so effective in their counter style as he'd often have 20-30 yards to use his pace to run into, Arsenal play a system in which they're often camped inside the opposition's half looking to break them down, so the space for Vardy will be much more limited. He may well be able to adapt to that easily enough and use his pace to run off the defence and get a shot off but I think at £20m for a 29 year old, it's a huge risk on Arsenal's behalf to be signing a striker that flourished in a completely different style.
Of the "big 3" players at Leicester, I'd have thought Mahrez would've been the one they'd try and pursue, With Sanchez and Ozil part of that supporting trio behind the striker, adding Mahrez to that would create an unbelievable triple threat.