I've been playing the most recent TR build for a week now and there's still content left to do in the first two cities I visited (Andothren and Old Ebonheart).
The last time I played TR I didn't talk to a lot of NPCs, just walk around and explore, because I was of the impression that quest content is still largely unfinished.
I was wrong.
There's so much quest density in the cities, you can spend a lot more time in them than in any vanilla Morrowind city, except maybe Vivec. And even the fetch quests are usually interesting.
Go deliver 5 bottles of wine to a tavern! Oops, the tavernkeeper expected 10 bottles, the merchant must have mixed the orders up, gotta hunt down 5 more.
Go deliver an ebony sword to a mysterious client! But wait, what's that - the sword is a fake, it's just steel made to look like ebony! The merchant is a scammer!
Lots of cool little twists on the delivery quests to make them less mundane. And usually, when a quest leads you to another town, you'll find other mini-quests or interesting locations along the way.
The quality of quests is, in general, above Morrowind's average. Granted, most of Morrowind's quests were extremely basic fetch and kill quests, but TR takes the same concepts and makes them more interesting with little twists.
TR also makes much more extensive use of Morrowind's dialog choices. It has always been a function in the game, but very very few vanilla conversations actually give you dialogs where you must make a choice. In TR, almost every quest has at least one of these. And very often, you can attempt to persuade an NPC to give you something or tell you something, and the likelihood of him agreeing is based on his reaction score towards you, so speechcraft actually becomes useful.
My favorite questline so far is Andothren's thieves guild. The guild was driven out by the Cammona Tong and you're tasked with re-establishing a foothold. Recruit new members, disrupt Cammona Tong operations, take over their smuggling business, etc. Some of the quests even involve choices with minor consequences (get rid of the Tong's skooma brewer - it's a khajiit they keep as a slave, you can either kill him or free him, and if you free him he arranges for your guild to receive regular skooma shipments).
My favorite city as far as quest content goes is Old Ebonheart. It's chock full of stuff to do. Lots of tiny little side quests, also several factions you can join (and they plan to make another, as of yet unjoinable faction, the Imperial Archaeological Society, joinable later, with quests and everything). I did Imperial Legion quests there, as well as East Empire Company quests, and a whole bunch of smaller side quests, some of which lead down into an extensive sewer network that connects to several basements so you can go and rob shit if you're so inclined. Apparently the thieves guild has their base in the sewers but I haven't found a way to access it yet. I also found a mysterious sanctuary that had nobody in it, so maybe that becomes important later.
There's been enough talk about making a new project for Vvardenfell once the mainland is done that I don't think you'll need Rebirth unless you're partial to it for whatever reason. Most of what I've heard has been about bringing the island more in line with what concept art and the beta suggested, along with a general TR-ification of land/quests/etc. But we're at least a decade away from that.
There's already a finished mod for Solstheim (the Bloodmoon expansion island) called Tomb of the Snow Prince. It's not officially affiliated with the Tamriel Rebuilt or Project Tamriel teams, but they endorse it as a high quality overhaul of that island's landscape. Haven't explored it yet so I dunno if it adds new quests or anything, but according to the description it tries to bring all of Solstheim's content up to par with modern TR quality.
https://www.nexusmods.com/morrowind/mods/46810