Hehe yeah, we get this question a lot.
Bottom line it comes down to tax treatment. That is the biggest factor - in a TFSA where there is little tax implication, then its not as important. BIPC was created specifically for US retail and fund managers to better invest in the company as there are restrictions for them around funds. By introducing the corporation, now US investors can more easily access the stock. That is why it was done in the first place. For Canadians however, its not as important, especially when holding in a registered account.
WHen BIPC was first introduced, it traded at a pretty significant premium to BIP.UN. When anyone asked, I said that while a premium may be deserved due to favourable tax treatment but it got as high as 30% - it was way overdone. If they are expected to be economically equivalent why would a Canadian pay a 30% premium for one over the other? I always said, I'd buy BIP.UN vs BIPC in that instance in a heartbeat (or BEP.UN vs BEPC which was the same scenario). Because of the big gap, BIP.UN had a higher yield and if held in a registered account, I felt that paying 30% premium for BIPC just wasn't warranted.
Fast forward today and sure enough, BIP.UN has closed the gap considerably. In fact, YTD, BIP.UN is sitting on gains of 12% vs the 18% loss for BIPC. Since the split, the gap is now only 7.1% - which is much more reasonable. I'd now expect them to both track each other moving forward. However, it would not surprise me if the markets acted irrationally again and bid up BIPC - time will tell.
Circling back to your question - there is not a clear answer. However, for simplicity sake if holding in a non-registered, than BIPC may be the better option since the dividend is an eligible dividend and not complicated whereas BIPC is a distribution and much like a REIT contains several forms of distributions (dividend, roc, interest, etc) which makes for more complicated tax reporting.
Mat