This is an interesting question which I've been asking myself every month or two for the last year or so. It's not straightforward. Some things to consider:

Vector tiles vs raster tiles

Mapbox Studio only does vector tiles, TileMill only does raster tiles (and static images)

Neither of those things will likely ever change. I thought MS had a way to generate a PNG export, but I can't seem to find it now.

Support for vector tiles in existing GIS packages is still pretty basic.

Local data sources

With Mapbox Studio, you can't really have a private data source with public maps - the data itself will essentially be exposed to the public. That's bad if your data is somehow private, and it's bad if you can't afford to host it all on Mapbox's servers.

Web based assets

TileMill used Millstone to fetch web assets, so you could do: polygon-fill-file: url('http://...'). Mapbox Studio is strictly local only, and they have no plans to change that.

Hosting your own tiles

It still seems to be pretty tricky to host your own vector tiles. PGRestAPI does it (apparently, I haven't tried), and I think somewhere in the Mapbox repos is the bit you need, but it doesn't seem that simple to me.

Hard to build your own data source

Maybe I'm doing it wrong, but I find it very fiddly to build data sources with MS. The Tilemill approach definitely had its drawbacks, but it was very easy to add and remove layers. The PostGIS support feels clumsier (maybe just the lack of the bookmarking system...)

Integration with mapbox.com

Overall, it seems harder to work independently from mapbox.com. Obviously that's a totally legitimate business decision.

This is an interesting question which I've been asking myself every month or two for the last year or so. It's not straightforward. Some things to consider:

Vector tiles vs raster tiles

Mapbox Studio only does vector tiles, TileMill only does raster tiles (and static images). There is a raster tile endpoint for Mapbox Studio now: https://www.mapbox.com/api-documentation/#static

Support for vector tiles in existing GIS packages is still pretty basic. And of course you have to figure out how you want to style them, if you're not using Mapbox-GL-JS.

Local data sources

With Mapbox Studio, you can't really have a private data source with public maps - the data itself will essentially be exposed to the public. That's bad if your data is somehow private, and it's bad if you can't afford to host it all on Mapbox's servers.

Web based assets

TileMill used Millstone to fetch web assets, so you could do: polygon-fill-file: url('http://...'). Mapbox Studio is strictly local only, and they have no plans to change that.

Hosting your own tiles

It still seems to be pretty tricky to host your own vector tiles. PGRestAPI does it (apparently, I haven't tried), and I think somewhere in the Mapbox repos is the bit you need, but it doesn't seem that simple to me.

Hard to build your own data source

Maybe I'm doing it wrong, but I find it very fiddly to build data sources with MS. The Tilemill approach definitely had its drawbacks, but it was very easy to add and remove layers. The PostGIS support feels clumsier (maybe just the lack of the bookmarking system...)

Integration with mapbox.com

Overall, it seems harder to work independently from mapbox.com. Obviously that's a totally legitimate business decision.