Axminster over Proxxon for my money any day. But both have been discussed here recently.
Have a look at these threads.
http://www.penturners.co.uk/turning-pens/19222-small-space-lathe.html?highlight=proxxon
http://www.penturners.co.uk/tools-equipment-and-accessories/19237-axminster-precision-lathe.html?highlight=precision
Putting proxxon or precision pro in the search box nearat the top of this page will bring up quite a few other threads about them both too.