Bormio onwards......
Hi, for what it's worth, I would go the Gavia route.
Here's why, since the Top Gear crew did the 'greatest driving roads' episode, the Stelvio has become popular and in fact it is great - to look at !
The view down over from the top is something else, fantastic. However, IMO the truth is that the road up from Bormio is better.
We did both of these passes a few years ago, went up from Bormio and down over the Stelvio, we intended to go back up but the road was crowded by 10.00am with bloody coaches among other vehicles and they struggle with tight hairpin bends, so we 'happened' to find the Gavia on out way back !
Even now, several years later we still refer to it as the Goat herder pass, in places it is barely wide enough for one car width and we met traffic on it ! But for the views and the thrill - areas of sheer drop and NO barriers, it is hard to beat.
All joking aside though, both are great, the Stelvio is probably on everyone's bucket list, do them both - and every other Pass you can find - they are all great !