Why EPS is quite the same for the peer stocks despite of different number of shares and share prices?

Please help me to figure out EPS issue. Googling didn’t help me, all hope for you.

Company A earned $10 bln, it has 1 bln shares. Its market cap is $100 bln, share price is $100.

Company B earned $10 bln, but it has 10 bln shares. Its market cap is also $100 bln, share price is $10.

These two companies are quite the same but EPS of company A is 10. EPS for company B is $1.

How can you compare EPS of companies that are free to choose the number of stocks they are willing to issue?