It doesn't seem to work!
itunes keeps telling me that the sim card from sunrise is not supported.

I've already been twice to swisscom and they ensured me that the phone is unlocked (the second time they kept my phone for an afternoon); I've been to sunrise and phoned them couple of hundred times but they aren't helpful at all..

Does anyone has a successful story to tell me or should I give up?

When the iPhone has the SIMlock removed from it, you must sync it a couple of times with iTunes and the lock will then be removed. I did this a couple of years ago and it worked reasonably well.

It's a 3G or 3GS, I'm guessing?

I've synced and restored it a couple of times. One of these times it went into emergency calls only and that's when I brought it back to swisscom the second time and they kept it for one afternoon.
I went to another swisscom shop today (as I was in another part of the town) and they asked me to fill an online form. Now I need to wait more days for a response..

it is a 3G. I've got it from swisscom almost four years ago..