Founder at Tinkerbox
Next and Gatsby come in pretty close when it comes to a lot of the front-end features, with a lot of it in favor of Gatsby. However, Next comes with first-class support for Server-Side-Rendering (SSR), while it's a bit of an afterthought in Gatsby; a lot of Gatsby's features wins are also nullified if you attempt to do SSR.
Ultimately, with Next if you want to get to the same level of polish that a Gatsby site you'll have to put in some hard work. Next is simple enough to get going and does a decent job dealing with SSR, which can be painful to deal with. I don't have first hand experience, but it's probably going to be a lot more painful trying to do SSR in Gatsby.
However, I do think that SSR is the future, for now, and Next provides the best developer experience in that regard.