The main advantage is that a node can be established in the browser without an extension (and more specifically a node can be established in any JavaScript ES6 capable environment). This means you can send a transaction from practically anywhere, and you don’t need to rely on a third party to relay your transaction to a node.
All other advantages stem from this first one. Websites can mine in the background as a form of monetization (although not very profitable with GPU miners existing), websites can monitor and interact with the blockchain without their users needing to do anything other than visit the site, developers can easily work with the blockchain since JS is a friendly and easy to learn language, etc…
Personally, I think Nimiq’s strength lie much more in it’s focus on the end users (nimiqons, keyguard, etc…) than on the fact that it’s a browser based blockchain.