The size of the robot

Can a smaller robot (38x38 cm) be better than a bigger one (45x45 cm)for the competition?

Yeah, having a smaller size can help you in many ways. For example, in Toss Up season, having your robot under 12 inches helped a lot because you could go underneath the barrier. This year, a smaller robot could possibly help you hang easier, because it will probably be lighter

I am not sure that size matters that much. It really depends on your design and what you are trying to accomplish. A very well designed robot will compete regardless to the size. There are certainly some advantages and disadvantages for a smaller robot vs. a larger robot.
lighter - easier to climb (if you choose to)
faster for a similar drive train
maybe more maneuverable
limits your space for attachments/manipulators
if you are going high with your mechanism, might be easier to tip

You need to decide based on what you would like your robot accomplish, then design around that. That will dictate size.

It’s not a bad idea to shoot for 17" or 17.5" so when you get to inspection you don’t find yourself having to hacksaw a piece from a late-addition or miss-measuring. Every year, it seems that at least one team is scrambling at a competition to get legal: especially last year when expansion wasn’t legal, a couple teams had not accounted for intake flappers going out of the 18" zone.

The rule I set for my team is that the limit is 17.5" on every side, just so the novices are aware of clearances