Any reason to use TileMill if Mapbox Studio is meant to replace it?
TileMill is designed for producing raster tiles. It's powerful and easy to use with CartoCSS and I found it ran well with no bugs (PC version). It's also pretty well documented, with lots of examples and the tiles produced are easy to integrate with Leaflet.js web sites.
Vector tiles potentially offer many advantages, in terms of styling flexibility and new interactivity. But at the moment there are many restrictions in terms of the number of layers, and the amount of geometry you can upload to Mapbox through Mapbox Studio. There is also a real lack of examples at this early stage.
Mapbox's business model is based on them hosting your map data, and there are understandable business reasons for their switch towards vector layers. TileMill layers can be exported as .mbtiles and hosted elsewhere. I do hope TileMill is maintained and updated as it's a great piece of software that Studio will do well to match.
I am a long time user of TileMill which is a great tool. After spending two weeks testing MapBox Studio and I can say it was a huge disappointment.
1) It is so buggy that it is practically unusable, both on Windows and Mac versions (and especially on Windows), the program literally crashes every 2 min.
2) The interface is less intuitive and practical than TileMill. It tooks me a while just to understand how to import a simple shape. With Postgis, you will have to re-enter the entire connection parameters for EACH table you wish to add, this is crazy.
3) You can export your shapefiles to a vector tiles db, but then you have to upload it on mapbox server if you wish to style the tiles. This is the biggest concern at the moment as the available space on your mapbox account is ridiculously low and so expensive ($499/month for 30Gb, are you serious ??). I made a try to export my project in vector tiles, the size was about 300Gb, so am I supposed to pay $5000/month just to work with my own data ?
4) Vector tiles are not safe. As they contain vector information, anyone can easily process them to rebuild your original shapefile. Not a big deal if you are using open data like OpenStreetMap but a way too risky if you work with valuable proprietary data.
So I will continue to use TileMill. Unfortunately the program has not been updated for 2 years now, and likely won't be anymore as it is not compatible with MapBox current business model.
You may be interested in Kosmtik, which is an alpha project with similar aims to TileMill and under active development.