Hard question and I went myself through this process two weeks ago.
At the end I had Wordpress and Tumblr on the shortlist and went for Tumblr finally. At the end it heavily depends on your requirements. If want to self host and are heavily into SEO and customization then rather Wordpress, if you want built-in virality, a huge community and a social network touch then Tumblr is your friend. Both are quite powerful but I liked Tumblr a bit more because it feels/looks fresher and I needed it for a private blog and not for creating tons of traffic. Then I'd go for Wordpress with a custom domain and selfhosted.
OK, if it wasn't clear that that was me being facetious then let me make it clear - I was being facetious and poking fun at the fact that people think Pinterest is 'for girls' ...jeez guys.
Incidentally I started my sexist Pinterest board last night, I have enjoyed using the platform thus far - the Chrome P button plugin is super handy.
For your specific use case, Tumblr is almost certainly the right call. It's a more capable platform than I think people sometimes see, even for long-form text, but "easily sharing photos and videos of things you like for no particular reason" could pretty much be Tumblr's corporate mission statement.
If it is not to contain words, do you really need a blog? It seems as though Facebook and Twitter are quite well suited for sharing photos and videos, among a million other options.
