The Emco lathes have a very good reputation for quality and accuracy, but of course a used lathe adds many variables related to its care and use. It sounds like yours has been well used and / or poorly cared for and is now in need of some serious rehab. The Emco Compact 8 was the inspiration for the very common 9x19, 9x20 lathes sold by Jet, Enco, Grizzly and others.
Brand new, I expect the Emco 8 would be more accurate than a Logan, but yours is well worn. A common complaint for the Compact 8 and related 9x19 lathes is rigidity or a lack of. A 10" Logan obviously has a larger working envelope, and being a larger heavier lathe will be more rigid.
Logan hasn't made new lathes since about 1970 so any Logan you find will be a minimum of 50 years old. You could get lucky and find one in great shape that is a huge improvement over your current lathe or find one in much worse shape. Logan's were made by Powermatic until the mid 1980s, but they dropped the 10" lathes early on. I have a Powermatic Logan from 1978 that was sold as a 10x24" but in reality it is an 11" lathe fitted with the smaller 1-1/2" thread spindle common to many vintage 10" lathes.
I also have an Enco 9x20 lathe which is very similar to your Emco Compact 8, my Powermatic / Logan is a substantially larger lathe, almost 60" when the base is included, also 3x the weight. An actual Logan 10x24 is smaller, the Logan site shows most of the Logan 10x24" lathes as being 43" long.
If the Logan you are looking at is in good shape, and has all of the change gears it could be a good lathe for you, particularly if you don't expect to do much threading and if the price is right. I agree with the others though, that the QCGB is worth looking for. It doesn't completely eliminate a need for change gears which will be required to do metric threads and some odd ball threads. The metric change gears for a Logan are quite expensive, something to think about if cutting metric threads is important to you. Logan does still sell parts and manuals for their lathes, not cheap but they are available. Scott Logan runs a Logan Facebook page and an IO groups (replaced Yahoo groups) group and actively responds to technical questions.
If you like the size of the Compact 8, you might look for one one of the Chinese or Taiwanese 9x19 lathes. They are basically the same design as your Compact 8 with the addition of a 1/2 quick change gear box. Fairly cheap new, Grizzly has their G4000 on sale for $1350, and they are quite common on the used market. A good Logan 10x24 is a better lathe, but a modern 9x19 will be able to cut metric threads and it is pretty much the same size as your current lathe. A 9x19 also might be able to use some or all of your existing tooling.
