Having used both of these services, NameCheap is the better option in my opinion. They're cheaper, offer WHOIS Guard for free for the first year (usually), have cheaper SSL certs, and their ethos is much better than GoDaddy's. GoDaddy's interface changes far too often and usually for the worse. Their domain purchasing process is OK, but their admin panel is strange and doesn't always make the most sense. Their hosting is ATROCIOUS and plagued with slow speeds and unreliability.
Besides GoDaddy offering sub-par service, the marketing they use is typically degrading towards women, and they not only supported the terribly infringing SOPA bill, but they basically helped write the thing. There's pretty much nothing good that I can say about GoDaddy.