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.
You could do that just as well with teleportation, possibly even better depending on what security measures you need to bypass. Teleport in, plant a bug, dig through their computer for anything incriminating, teleport out.
Of course, obtaining evidence in this way makes it illegal to use in court, but that doesn’t really matter because the people you’re after will never be taken down in court anyway.
That’s why I said citizen journalist. Exposing corrupt people in the news is a major step towards criminal court, and even if there is no case, public opinion can be swayed and that’s a death sentence in many ways.