Stability is a combination of all factors, weighted towards their contribution to the overall $\Delta G$. In this case ring strain is a major issue, and one not necessarily likely to win out over the tertiary -> secondary carbocation transition you've drawn (the bromine has a lesser role to play as well, as you highlight). An equilibrium will form between two drawn structures. Absent modeling I can't give hard numbers, but my intuition is that the cyclopentane will be the more stable.
Ultimately though you're missing the greatest contributor to a beneficial $\Delta G$: quenching the carbocation. Whether or not you get a cyclopentane/cyclopentene is going to depend on how quickly a proton can eliminate from those methyl groups to form a terminal alkene. In most cases I think the 1,3-carbon shift is going to be faster, but not by much when there's six potential protons that can eliminate.
As with most carbocation systems you're going to get a mix of products.