I have used the 580P together with the 625XT to test both on run and bike rides.
While the 580P has advantages like a better used scree, barometer and ANT sensors, the 625XT is a better overall device.
1. Is there meanwhile a way to purchase the GB-580 with a wrist-strap as well (I read it was not one year ago, but there was picture showing one)?
Dont know, but even if it fits the gb580 is a little thick for the arm.
It fits well in the hand though.
2. Is it true that the device uses less accurate GPS sensors (or measuring/calculating method) than the GH 625XT?
SirfStar3 vs SirfStar4. That should not be major, but I expect the 625XT to have a better antenna too. The track in the woods is often a little off compared to the 625XT (why I suspect the antenna). Road tracks are fine.
The SW is tweaked for "road usage" it seems. While a pace value can be displayed, it does consistently seem a little slow.