You could turn invisibility on and off as you like and there would be no time limit. Your clothes would turn invisible too, and you could decide whether the items you are holding would be visible or not.
There would be no limits on how many times or where you could teleport. The items you hold while teleporting would be teleported too. You would also have the ability to know if the place would be safe to teleport to, so you wouldn’t teleport and get impaled by an icicle or teleport inside a wall and get your insides filled with concrete or something.
Personally, I don’t know which one would I pick. Invisibility would be awesome for pranks and stuff, but teleportation probably would be more useful for everyday life.
Teleportation. Invisibility is a nice gimmick (until you accidentally leave it on and get hit by a car, that is).
Teleportation isn’t just incredibly convenient, depending on the distances you can travel in one hop it’d also save you a lot of time (skip your commute, instantly travel to a nice vacation destination and back), and it’d be a money maker (fastest courier in the world).
Even if it was just line of sight, being able to easily reach places that are normally hard to reach or require extensive detours would be helpful. Even just crossing a busy street without having to wait for the traffic light would be a nice thing.
I would teleport to Japan to eat all my meals. So much good food for so cheap.