The downsides of a "public" registration are that you may get some extra spam email at the emails listed in your WHOIS info.

Spam filters are pretty good nowadays, though, so who cares.

Plus, here are some downsides:

1) It's harder for an interested party to contact you to buy the domain.

2) On Godaddy hosting, it took a little while longer to transfer the domain to a buyer (for me), becaue I had a little trouble getting my domain off the private hosting -- I had forgotten the password.