If both Tarp & Barrett make it out of TC in one piece, then there could be one spot open for either one or the other: whoever displays better ST skills, better coverage skills, and - perhaps most importantly - better tackling skills. And based on the little we saw of Barrett last year, I would say that he is likely behind Tarp in the tackling department, unless Tarp is a really, really bad tackler.
I tend to agree with this, though others may not. I can see the Pats having a defensive roster that looks something like the following:
6 DT/DEs: Wilfork, Love, Fanene, Pryor, Deaderick, Warren/Brace
4 DE/OLBs: Jones, Scott, Bequette, Cunningham/Carter
6 LBs: Mayo, Hightower, Ninkovich, Spikes, Fletcher, Carpenter/White
1 SS: Chung (Tavon Wilson or a hybrid LB/S could back up Chung)
6 hybrid CB/FS: McCourty, Dowling, Gregory, Wilson, Moore, Dennard
1-2 CB/slot: Arrington, +/- Allen
0-1 hybrid S/LB: Tarpinian/Barrett
In this scenario, Tarpinian and Barrett would essentially compete for 1 spot as a hybrid LB/S in the Tank Washington kind of role, and would also back up Patrick Chung. Barrett has had trouble staying healthy. Both guys are athletic and are excellent STers. The Pats could also opt to keep neither and could keep Will Allen as an extra CB/slot CB.