No way to guess without being able to shoot the particular snub. How experienced of a revolver shooter are you? How about been experienced with the smaller 5-shot snubs? Even some experienced revolver shooters of med/large revolvers find the smaller 5-shot snubs to be a bit harder to shoot.
In my handful of snubs which are rated for +P, the Rem Golden Sabre 125gr +P's are accurate enough to use for shooting at wooden clothespins at close range (out to 5yds), but so are the Speer GDHP 125gr & 135gr +P's, and the Win 130gr +P's (RA38B/PDX1).
I've got a couple of standard pressure 110gr JHP's (Fed & Win) that seem to be quite accurate in a couple of my J's, and which I save for a 37-2DAO I ordered which isn't rated for +P (according to someone at the factory, who looked it up and called over to Revolver Production for me, since I was calling as an armorer).
The standard pressure 130gr ball loads are a little less accurate, in some of my snubs, but some of the Win 158gr LRN/LSWC standard pressure loads have also been pretty accurate in some S&W J's, as have the Win & Rem 158gr LSWCHP/LHP +P's.
If you're right-handed, is the shorter trigger reach and DA pull of the Taurus snub causing you to pull the muzzle off to the left when the snub fires? Is the increased felt recoil of the +P loads causing you to have that last moment flinch (tightening of the grip, which may also be affecting your trigger finger's last bit of press)?
No way to really guess, though, without being able to watch you shoot, from both sides and a couple of angles (watching your hand & index finger during follow-through), and being able to shoot the gun using the same loads.