When you make a PVC connection, the cement acts like that you may have used as a kid making model airplanes...it melts the two pieces together. While it may be a weak point, it makes a mess when you try to get them apart since they are effectively welded together.
Sometimes, you can saw through the vertical portion of the flange a few places and pry it off.
An alternative is possibly to use a RamBit to bore out the old vertical riser (assuming they used a riser and it isn't an elbow), then you could install a new vertical piece of pipe and a new flange.
A picture would help.
Is there a vertical piece? Can you see the edge or the socket of the fitting below?
A properly installed flange is sitting on top of the FINISHED floor, and anchored through it into the subfloor...then, you'll have easy choice and any toilet will fit.
Depending on what you have, you may just decide to cut a hole in the basement ceiling. Unless it is textured, it isn't all that hard to patch seamlessly. Texture takes some skill to match.