I've owned a Taig and I have a mini-lathe.
The Taig is precise out of the box, but the lack of a screw drive is a major problem. No thread cutting and no mirror finish parts. It's virtually impossible to hand crank slow enough to get a piston like finish. The factory chuck is only ok, but without collets it is far less precise than the rest of the lathe.
The mini-lathe should be considered a "kit". It needs to be tuned up. It will hold tolerances quite well if some attention is paid to it. The factory chuck is not ok. Either get a good quality Chinese four jaw, or one of the European (likely Poland) 3 jaw chucks. However a 4in Bison 3 jaw chuck will cost about 2/3 the price of the lathe.
A mini-lathe with a couple of modifications (better chuck and tapered roller bearings in the head is a pretty good lathe. $1000
The Taig with the addition of the compound slide and the screw drive still won't cut threads, but is otherwise a very good, but very small lathe. $600
If just the headstock, bed and crossslide are considered on the two, they are just about the same quality. The mini lathe has more parts to go wrong.
By the way, the chuck on the Taig I had was hard to tighten. It operates more like a drill chuck. No key, just a bar to hold it while it is tightened with the hands.