Thank you and offer dilemma

I would like to thank everyone on WSO for support and knowledge I gained from by reading the forum regularly. I am a Canadian and I went to a target for grad school. After many months and having several offers being revoked due to Visa issues, I managed to get 2 offers (not in writing yet):
1) Big 4 pharma risk consulting - I reached out to an alumna earlier this spring, had a very nice chat, and thought it ended there. After about 4 months, she reached out to me and asked if I was still looking for a job, I said yes, so she brought me in for an interview. I liked the team, the director was really pushing for me, and the firm has no problem in sponsoring my Visa. I am not too crazy about the work, and after all it's consulting, so there will be quite bit of traveling. However, I told the interviewers that the firm is my top choice and I sorta verbally accepted.

2) Healthcare ER at a boutique - This is what I am really passionate about. After several rounds of interview, the Senior Analyst asked me to be contractor, then offered me a full time position (right after I vaguely verbally accepted the first offer). Again, I am worried about the Visa issue (although he said the firm is cool with it) and the risks involved.

Any advice would be appreciated.