The hardware and tool stores that I have seen selling these chinese machine tools seem to let real idiots set them up for display. Normally the machine comes covered in red grease, with some casting sand in the nooks and crannies, and all the handles and knobs either reversed or removed. It would seem a no brainer to me to take a half an hour to set up and adjust the machine to be some what representive of it's out of the box potential. Sadly this seems to be asking too much, as normally the machine feels like a real piece of junk.
The slop in the cross slide of the 7X is normally from two "features". The cross slide nut is designed to be tilted with a set screw in the middle and two retaining screws to remove the backlash.
The second feature causing backlash is the lack of a decent thrust bearing set up. Just lapping the standoff can address this, but a better solution is to add bearings to the standoff.
http://www.mini-lathe.com/
I can't give you a qualified comparison to the proxxon or lathe master 8x14 because I have never used them. You really don't see much info on the Proxxon's n the web. The lathemaster 8x14 has a pretty dedicated following.
Do you get many Emco Compact 8 and compact 5's in the states? The compact 8 was supposedly the lathe the chinese copied for all those 9x and 8x models.