Why B2 is more stable than Li2, though they have same bond order?

 if the bond order is the same (your case), you can not talk about stability using those diagrams.

Coming back to the question, looking the dissociation energy (the energy relative to separated atoms) for B2, you will see it is bigger in module. So it will be more stable. I do not have a qualitative way to estimate which of those molecules is more stable.

The way to know it theoretically is using electronic structure programmes.