r2modman and ThunderstoreModManager are the same thing, except ThunderstoreModManager comes with the "Overwolf" overhead--recommend to just use r2modmanager there.

I have not used Nexus' mod manager (Vortex), but I avoid using Nexus ever since they ticked off a bunch of mod creators by claiming rights to all mods uploaded there. One thing Nexus DOES have over Thunderstore (for the sites, anyways, not the manager) is that you can post and read comments there, though.

You can still use any of the Mod Managers AND use mods from the other sites simply by dropping the DLLs in your plugins folder; they just won't have benefits like allowing you to auto-update the mods.

All things considered, I personally prefer r2modman. Since I no longer do Nexus, I can't say for sure if it's more up-to-date or not.