Wget does not validate certificates by default because there's no CA bundle provided with wget. It does check for /etc/ssl/cert.pem, but it doesn't provide one. So you have to provide one or set up /etc/ssl/certs/ as OpenSSL libraries expect.
Curl does provide a CA bundle (/usr/share/curl/ca-bundle.crt) and by default libcurl validates certs against it.
cURL doesn't provide a CA bundle any more [1], it's the job of your OS to provide this. As I understand it, all tools that provide SSL support will fail safe if there are no root CAs on your system.
[1] http://curl.haxx.se/docs/sslcerts.html
But the point halfasleep is making is important: Don't assume either wget or curl will validate your SSL connection because it may not have been set up by your OS/distribution.