I'm getting a new computer and I'm thinkng of using Mod Organizer this time instead of Nexus Mod Organizer. I've heard that there are some problems with using the creation kit with it. Have these been solved? I've a half completed mod I'd like to transfer over and finish. Can you use both? Mod organizer for your downloaded and finished mods and the Nexus organizer for your work in progress? If it is a problem I'll stick with Nexus.

You can't use both AFAIK, when using MO the data folder remains in a vanilla state - nothing is ever added to it. Unless the newest versions of NMM use a similar system, I don't think using both is a good idea as mods in MO don't actually every reside in the data folder for a normal launch of the CK to find for editing. Do note that I haven't used NMM in some time now so my information on it may be out of date. There was a major update to NMM in the last few months with improvements in anticipation of Fallout 4's release, perhaps things have changed on that front.

Regarding the CK and MO, I've been using them together for sometime to work on various mod projects of mine and haven't run into any issues, the CK start up and initial responsivness is slightly slower than a standard use startup due to the virtual file system, but once you've got the CK running it performs exactly as you'd expect. You'll need to be aware of how the override folder works when saving any mod work you've done in the CK, but that's part of the general MO learning curve anyways.