I've owned tandems with both STI's and bar cons and I currently own one of each on single bikes so I've had a good amount of experience with each.

A while ago, I was forced to make that very decision regarding my tandem. I wanted to install Magura hydraulic brakes, but that would have ment giving up my STI's. In the end, I forewent the Maguras because I loved the STI's too much. I also love my Flite Deck computer's gear indicator.

All of my tandem riding is essentially day rides. If I were planning a cross country trip, I think I'd take the opposite approach and use barcons. The thing that I like least about STI's is that when you get dirt and grime inside of them, they tend not to shift right. The last thing I'd want on a cross country trip would be to be stuck in Nowheresville, Kansas on a Friday night with a trashed out Ultegra STI.