Voted for the second option. Wrapping around might be too much and termination could be awkward.

How messy are you when cooking? First and foremost a backsplash should be functional- it should protect your walls from grease, food and water spatter. So if you expect that area of the counter to see hard use (perhaps a coffee maker will live there?), then put the back splash all the way around.

If that area of the wall won't be subject to spatter hazards, then it's totally an aesthetic decision. And that depends on the tile you're using. Is it eye-catching or subtle? Is it going the full height of the wall or just to the bottom of the hood?

Me, I think I'd do a plain tile, full wall height and to the end of the counter. Outside corners aren't that hard, especially if your tile has trim pieces available. And even if it doesn't, there's probably an unobtrusive Shluter trim that would work.

I voted for option #1 because I believe it will look better!