I own both guns you asked about -- Taurus 85UL and Bersa Thunder. Each is a good value.
I pocket carry, using a pocket holster. I like the Taurus better for that method. It is lighter than the Bersa and its rounded shape is less conspicuous in a pocket.
Also, you can use .38 Special +P ammo in the Taurus. I practice mostly with std. pressure .38 Special but include 5-10 rounds of +P carry ammo in each practice session.
While there's some quality .380 ammo out there (I like Cor-Bon JHP; want to try Cor-Bon DPX), I do not share Horge's view that:
the ballistic and terminal effects difference between .38 and .380
is negligible
There's stuff in .38 Special +P I'd definitely rather deploy than a .380, like the Speer 135 grain "Short Barrel" Gold Dot and the Remington 158 grain pure lead semiwadcutter +P hollowpoint (Rem. Item No. R38S12). Good penetration, good expansion, and heavier bullets than any .380, with more radical hollowpoint shapes than could feed easily in a semi-automatic. Lots of older LEOs sing the praises of the 158 grain lead +P hollowpoint's stopping power. 158 grains of readily expanding bullet at 800 fps from a snubby can be expected.
On the other hand, in my experience the Bersa is easier to shoot accurately at speed. It is a reliable little pistol. Mine has fired 500 rounds and only jammed once (a failure to feed with factory FMJ -- racking the slide cleared it). The Bersa is also more fun to plink with. New shooters I've taken to the range have liked it.
Interestingly, I find the Taurus at least equal in intrinsic mechanical accuracy. I can cock the Taurus's hammer, aim carefully, and make surprising hits on smallish targets out to around 20 yards.
Both good guns.