Personally, I use PES and TESNexus.
I feel that the nexus has the most comprehensive controls for displaying and managing your mod's download page. For files under 2MB, people downloading don't have to register with TESNexus. Unfortunately, Nexus has implemented a very annoying feature. If you are not registered, you have to sit through a 40sec or so ad before you can download. If you are registered, you don't have to put up with that except for really big files (I haven't research the file size threshold for ads for non-premium members). It's been a while since I did more than post my mods there, but back in my TESIV downloading days, I found the staff to be very responsive when I reported abusive comments. You do not have to wait for your files to be approved: upload is instant. Updates are also instantly "live" - which makes the "hide your mod from public view" option very handy when you have to update several parts of your mod's download page. I prefer it's rating system (a simple "endorse" or "do not endorse" this file) to PES's 0 to 10 arbitrary grading scheme.
PES doesn't have the same amount of control over the download page. Anyone who wants to dl needs to register with File Planet, regardless of file size. Unlike Nexus, PES now has a feature where you can upload ginormous files (no file size limit), which is good if you plan on making mods with lots of textures and models and don't want to break it up into Part 1, Part 2, Part 3, etc. People downloading from file planet don't have to sit through an ad, though every once in a blue moon someone will come on these forums and be under the impression that you have to pay to be a member - a symptom of File Planet's constant push for people to register for the pay-for-better-service subscription. APY and the staff are very responsive when it comes to you reporting site problems or abusive comments/people abusing the voting system. You have to wait a period of time before your mod goes "live"; file planet has been having brain farts where you have to wait about 10 min before you can actually download (without getting an error) any files that you update. :shrug:
Search system: Nexus' advanced search is more comprehensive than PES's currently. Not that you'd want to use anything other than ES Search 2.
But, to be fair, there are a few mods that don't seem to pop up on ES Search, despite their existence on PES and/or TESNexus.
I personally do not use ElricM, since my control over the mod is extremely limited (no screenshots, must contact site admins in order to update mod, poor user participation in the voting system). Perhaps it will update with better features one day. Naturally, being one of the first sites of the Morrowind modding scene, it is a grand repository of older mods that aren't around anywhere else.
Another site is that GHF and the Morrowind Modding History - I've heard great things, but haven't uploaded my stuff there, mainly because I can only keep track of so many download sites, and updating a mod would become quite the project if I have to update it across three different systems!
Problems: people who are not registered have download limits. However, the few times I have tried to dl from there, it says I've reached my dl cap - even when I never downloaded anything there ever before! =/ Not sure if it hates my browser and/or NoScript. At any rate, it hasn't been friendly to me, a non-registered member, whenever I have tried to download a mod. To this date, I have not successfully downloaded a single file from that site.
EDIT: Trying to remember if I registered... oh yeah, I think I tried, but it wouldn't give me a link to activate my account, so I still couldn't download diddly-squat. I'm sure I'll figure it out one of these days. All the problems could be on my end, I use several Firefox addons - NoScript might be making the site fussy, I don't know.