This is probably wrong, but my though process:
No of bitcoin addresses = X^length
length = 32
x is no of characters. Since you have alphabet + capitals + numbers i would say X = 62.
It has to start with either a 1 or a 3 though, so 2 * 62^31, right?
The reason bitcoin addresses are short is they are hash of an ECC public key. In order to sign a transaction you have to provide with your signature, the full (longer) public key, which is first checked to hash to the address, before being used for verification.
But Monero address aren't directly comparable to Bitcoin addresses in another way. There is an extra step in the handling of stealth addresses that uses the address (public key) to create a new one-time key pair each time it is used. Only the one-time public key goes on the blockchain, not the address itself. That's why it is said that payments are unlinkable: no one can tell by looking at the blockchain the address that was used.