* More fine-grained control of your caching is possible
* Easier to express normalisation of requests (increase your cache hit rate and protect your underlying origin from malicious requests by discarding cache busters)
* Inline C means you can do things like move your authentication to the edge
* In theory if you have enough RAM you can go faster than nginx's on-disk... in practice the sweet spot for the gain is small and they're both on par
But then... it comes with disadvantages too. Like most Varnish services would never let you do the nice Inline C stuff because no-one in their right mind would run untrusted code in their environment where it could impact another customer. If you see a provider do this (at any price point), avoid them.