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.
With the stipulations given here (no limits on where, and ability to know if it's safe) you could teleport to what astronomers speculate are earth-like planets. Grab some samples, head home, repeat. Maybe win the Nobel Prize for discovering extraterrestrial life.
Given that, it feels a bit one sided against the other option that would let you perv a locker room or get trapped in a bank vault when you trip a non-visual sensor.