Depends

First of all on linux/mac Nexuiz and ~/nexuiz is almost equal but the first dir is for all users, the later just for you personal. On windows you can use the startup command line paramater -mygames to make it use %APPSDATA/My games which then acts the same way as ~/.nexuiz (i hope it have that path correct)
The mappack on the official Nexuiz.com site is zipped and you need to unzip and put all the pk3 files into Nexuiz/data or ~/.nexiuz/data As a rule of thumb .pk3 files go into Nexuiz/data or ~/.nexuiz/data
downloaded maps are stored in Nexuiz/data/dlcache (well or ~/.nexuiz/data/dlcache)
Dedicated server use Nexuiz/data, ~/.nexuiz/data (or the one for -mygames) to look for pk3 files.. or load unpacked maps (.bsp files) directly in data/maps
Basicly there are no differences except that there is no ~/.nexuiz dir on windows and the APPSDATA one is just used if you use the -mygames parameter or nexuiz can't write to Nexuiz/data ..