So that's really odd; because conventional vs climb should just reverse the path direction; it shouldn't make any difference to the dimensions in the gcode. It's possible that when a part is actually cut, a small diameter bit may experience differing levels of deflection (meaning the two cutting paths might produce slightly different sized parts).
What I'm seeing in the two square gcodes you just posted look correct - that is, they're both following a path whereby they're cutting 0.75mm outside of the 0,0-50,50 square (0.75mm being the radius of the cutter), and there are a few moves where the cutter arcs around each corner before making the next straight move.
I.e. from a visual inspection only (I've not run them on a simulator) I'd guess that both of those files should produce the same size square. If in practice they're not then it's bit deflection. It looks as though you're cutting in depth increments of around 1.814mm, and with a feed rate of 6000.0mm/minute (assuming that is the format/style your machine uses). That feels exceptionally high to me; especially for a 1.5mm diameter bit. I don't have any of my CNC stuff on the PC I'm using at the moment, but from memory, I'd run a 6mm bit at around half that feedrate, and thinner bits much slower.
If I'm right with the feedrate setting, maybe try lowering it to 1500mm/min, and maybe a shallower depth of cut (rough rule of thumb is no deeper than the bit diameter) and see if the conventional and climb jobs now produce the same size part. If so, the problem is bit deflection.
My guess is that 1.5mm cutter would be bending like a wet noodle at 1.8mm DOC and 6000mm/min feed.