If you're a fan of the original trilogy, I would recommend Legendary Edition for a few reasons: combat is more streamlined, Mass Effect 1 is actually playable now, and the graphics updates make all three games look gorgeous.

It definitely feels like a more unified series in this edition as opposed to three games with a matching title. The streamlined combat REALLY helps with this. The way you fight in ME1 is the same way you fight in ME3 (disregarding omni-jel and user interface inessentials that somehow still made it into ME1). Leveling up is more simplified, and they changed the way XP is awarded so you can level faster (this is also an option you can turn off if you liked it the old way).

Mass Effect 1 received the majority of the work for these remasters and that's blatant upon game open. If you've played the original, you might remember how unfriendly the UI was, how clunky the combat felt, and the effing elevator simulator every time you went to a new area. Elevator simulator is now skippable; combat is doable, and the interfaces are made slightly more user-friendly. If you ever wanted to play the first game, this edition is the superior way to experience it for the first time.

Graphics updates include updated models across all games, updated interface graphics, updated level graphics, the list goes on. There's even ray tracing now. It looks gorgeous.

TLDR; If you love Mass Effect, Legendary is worth it.