I'm type 1 and I've been prescribed Victoza. I've been on it for about a year and a half now.
The first 2-3 months were hell. Horrendous sickness (nausea, vomtting &diarrhea and I could barely eat a thing. Once that had calmed down though, all was ok.
I went on it because I have insulin resistance as well as type1 so my insulin doses were very high. The victoza allowed me to drastically cut my insulin and helped me lose 2 stone in weight / drop 3 dress sizes / reduce my BMI from 32 to 27 (ish - I can't remember exact numbers!)
The delayed stomach emptying is the key thing for type 1s I think. It basically makes you feel full much sooner than you normally would, so your portion sizes reduce quite dramatically. Like I said, for the first 2-3 months I hardly ate anything, so no wonder I lost weight. but it was not pleasant and I found myself in a few bad situations with going hypo and not physically feeling able to put any food or liquid into my body without needing to vomit.
So in summary, hellish to start with, but considerable weight loss with reduced portion sizes and reduced insulin levels (which also helps with weight loss, since high insulin levels encourages your body to put on weight).
One final thing, it is VERY expensive and not all doctors / GPs will prescribe it for type1s. Indeed, it isn't licensed for use by type 1s. I was lucky that my GP agreed to prescribe it under my consultant's advice - not all GPs will do so.