Great Addition. Not a Replacement.
I have both. 2017 Giulia and 2018 Stelvio.
The Stelvio is a great car and totally beats out any of its competitors in terms of power, quality, styling, and overall value, but I could never have it completely replace my Giulia.
Doubt you have the same relationship with your Giulia as I do, but to make it simple, my she is my one and only love.
Went to Palm Springs twice this past week (about 120 miles from where I live), took the Giulia on the first trip and the Stelvio on the second (both of their first times outside of the city actually). The Giulia did very well overall, but I could tell she just wanted to go back to surface streets where she could really show off her acceleration and handling. The Stelvio, on the other hand, felt perfectly at home on the freeway. I have the biggest and fattest wheels available for it (20 inches), and the road noise wasn't bad at all. It remained super composed and relaxing to drive all throughout the trip.
Final Verdict: If you need a city car for fun short trips, get a Giulia. If you need a larger car for relaxing long journeys, get a Stelvio.
If you want to enjoy life to the fullest, get one of each.