I have the Unimat 3 lathe/mill, Sherline lathe and mill, and a min-lathe and try to use all three for what they were intended for. Whatever you choose, the three of the most important criteria I think should be considered are motor torque, rigidity, and available accessories. You'll likely be disappointed if your choice can't be met by all three.
I bought the Unimat 3 new back in the late 80s and have always been disappointed in the motor torque but impressed by the rigidity and design. In the past I only used if for very light work. I've upgraded it to DC motors within the last year so it has a lot more torque, variable speed, and very quiet. I intend to use it for the PM Model machines kits and other model building inside the house because of those advantages. If you choose the Unimat 3 expect to replace the AC motors with DC motors including new a power supply and associated electronics. Unimat 3 accessories are also very limited.
The Sherline is similar to the Unimat with a lot more power out of the box than the Unimat with a huge amount of accessories. I use the lathe and mill in the garage because of the size but rigidity suffers as the machine is pushed to it's limits causing damaged parts. It's also not as quiet as the Unimat with DC motors but is still quiet enough to use inside the house. Customer service is also available.
I use the mini lathe for larger work in the garage. It has quiet a few modifications to improve power and rigidity. The accessories are still plentiful but can't be used inside the house and not easily transportable. The handwheels are also a disappointment because they are not as smooth turning as either the Unimat or Sherline but the runout is better than either of the two at .0002" measured at the spindle.
Out of the three I would recommend the Sherline as a first choice. It can do everything the Unimat can do and more. The most significant advantage the Sherline mill has is the Unimat is limited 7" X axis, 2" Y axis and about 6" Z axis travel. Also keep in mind chips are thrown about a 10ft diameter. Another reason I keep these in the garage.
However, there's something about the compact size and footprint of the Unimat lathe/mill combination makes it too hard to replace with a Sherline for model building.