What, and you think you will get a single consistent answer to this question
Some will say the Stelvio is iconic and a "Must Ride" road, and others will say it is not so great but should be on your bucket list - I guess it is not on yours as you are happy to skip it entirely.
Based on that assumption I would take the Gavia for a couple of reason, firstly it is a beautiful stretch of road, not a scratchers paradise, but a wonderful ride through great scenery and typically devoid of traffic. Secondly it means you will not have the slog up the congested valley road to the even more congested Merano...
...instead you then take the (IMO) rather under-rated Passo di Tonale - if you ignore the typically ugly Ski Resort at the top - but this gives a handy place to stop for morning Coffee and it is worth checking out the Morgue / monument thingy up there. And a bit further on you will come across an old WW1 fort that is also worth a quick stop and a couple of pictures.
I have used both routes (The Gavia one this year from Dolomites to Livigno) and would not bother to take the Stelvio route ever again, but I have also been up the Stelvio before and therefore do not have to tick it off my list which makes the choice easier....
...What you could consider is running from Bormio up to the top of the Stelvio 1st thing in the morning, grab your Sticker / T-Shirt and then run back down again, especially if the weather is on your side, it is only about 20 minutes from Bormio to the top, so will add about an hour taking into account a few pictures and souvenir purchase - and you can come home with your own opinion of (half of) the Stelvio (And IMO the best bit is really the views from the top anyway)