If it pulled to one side OR the other, then it could be a front end issue (damage from a hard curb impact, etc.). Pulling to both sides is something else.
The differences in geometry between the two bikes isn't enough to make any difference in the handling that you could feel.
CBR250R
Rake = 25 degrees
Trail = 3.9"
Wheelbase = 53.9"
Front tire = 110/70-17
R3
Rake = 25 degrees
Trail = 3.7"
Wheelbase = 54.3
Front tire = 110/70-17
The R3's front tire is a Bias Ply vs the CBR250R's Radial tire. This could make a difference. Radials tend to be more stable than Bias Plys in the upright position, then some of them can have a noticeable rollover when they transition onto the shoulders of the tire.
The R3 is a very noticeable improvement over the CBR250R (I had one). Power is much greater and pulling (particularly on hills) is VERY noticebly better.
I also have a CB500X, same engine as the CBR500R but different geometry, and the R3 isn't comparable to it, power-wise. The 500s extra 8 HP (on the dyno) can be felt, as can the 500s extra 13.40 nm of torque. Plus, the 500s max torque comes at 7,000 rpm vs the R3s at 9,000 rpm. The 500 pulls better in all gears.
The two bikes (CBR and R3) feel very different. R3 feels more stable at freeway speeds and still has pulling power at 70 mph, whereas the CBR250R is pretty much tapped out at that speed.
I'd have a shop check out the bike via a test ride and frame/fork check......
My .02.