I'm a co-founder of netlify and happy to chime in.
Surge is a simple tool with a really awesome CLI for deploying static sites quickly.
At netlify we're building a larger platform for working with a modern static approach.
We have an integrated continuous deployment platform. That way you just link a git repository to netlify, and we'll do the build whenever you push to git and even give you preview deploys of pull requests.
We run our own content delivery network, which means a lot for performance, and can post-process assets to automatically serve them out of a larger asset CDN with far future expires headers.
Netlify has built in Let's Encrypt support with a 1 click setup. We'll do automatic certificate rotation and enable HTTP2 when HTTPS is turned on.
Our CDN can handle complex proxying and redirect rules. If part of your site need to go to a dynamic backend or if you need API proxying, a one-line rule can set this up. We can even handle gradual migrations from a dynamic to a static approach by proxying all non-static requests straight from the CDN to a dynamic origin.
Apart from that we have lots of extra features like built-in pre-rendering for single page apps, Geo IP based redirect and rewrite rules, JavaScript snippet injection for easy analytics setup, form processing, etc, etc...