-3.00 lenses are only -3.00 when you look exactly perpendicular through the
lens. That's why they're usually made with curved fronts, to "wrap around"
and keep your line-of-sight as perpendicular as possible.

Consequently, when you change frames, a different curve or a different
distance-from-the-eye can create differences in the vision because you're
looking at more or less oblique angles to the lens.

If your frame can be adjusted closer to your eyes, or bent at the bridge to
"wrap" better, the effect will diminish.

Consider paying an experienced optician to help you solve the problem.

-MT, OD