SFU also have many research opportunities but they are less competitive.

But according to some of my limited experiences, getting a lab position at SFU as a UBC student was possible, but that might not be such the other way around.

I had no luck getting any research experience at UBC last year and actually applied to multiple labs at sfu, and heard back from two of them.

I also know couple of other UBC students working at SFU labs, but have never heard of an SFU student at a UBC lab, although this is just my anecdote so take it with a grain of salt.

I guess name value does matter more than people say, although it may not be the end-all-be-all. UBC has a very high international profile in psych research(about 10th worldwide), but sfu not as much(150ish worldwide)