After running all of them several times, on both story and veteran (hard) mode, and completing most of the associated achievements, I find them... interesting. I'm still not entirely sure what I think of them though.
My first impression honestly wasn't that great. I kind of coasted through my first couple of runs, hardly even taking in what was going on. To avoid "spacebar please" issues, there are no cut scenes in these, with all story context simply being delivered by a voice-over from one of your Alliance members (Hylo, Theron or Lana). I don't exactly mind that, but it does make it easier to miss what's going on if you're late to zone in or get distracted by boss mechanics. After a few runs I started to pay more attention though, began to take note of more of the details and started to have fun with them. I'm just not sure how sticky the whole thing is going to be.
From what I've read and heard, Bioware's design goals for uprisings were to reuse existing locations that had been somewhat underused and to provide an alternative to flashpoints that was a bit more fast-paced, with less worrying about how to correctly handle trash pulls and more charging in and smashing things. I do think they succeeded at both of these goals.
There are currently five uprisings and all five locations immediately look familiar to the long-time player. Done and Dusted takes place on Tatooine and actually has the most "original" setting of them all as the compound you enter didn't immediately remind me of an existing location on Tatooine. Firefrost (five years of WoW make me want to call this one Frostfire all the time) is set on Hoth, in an underground forge which I'm pretty sure was used in an existing quest, though I can't remember which one exactly... I think it was either a bounty hunter class mission or a world story arc? Crimson Fang takes place on Port Nowhere, a location from the smuggler class story. (Where's Corso? He said he'd be there!) Inferno reuses the base inside the volcano on Ord Mantell, and Fractured recycles the Emperor's space station one more time.
As far as fast-paced goes, there is indeed no time to spend on planning pulls as a lot of them spawn in from different directions in the way with which we've become so familiar over the course of Knights of the Fallen Empire's chapters, but somehow it's not as annoying in a group because there's a kind of friendly competition going on as for who kills the most mobs the quickest. Elite mobs are almost non-existent but weak ones appear in abundance, turning many a pull into an AoE-fest. This could be boring, however the way things spawn and are spread out differently every time does keep things somewhat interesting. There are also three types of temporary power-ups that you can pick up from boxes throughout the instance, which add an additional way of sowing destruction and another layer of friendly competition for group members. ("Nooo, I wanted the rocket launcher!")
While there are many mobs per pull, the number of trash pulls itself is fairly small and you go from one boss to the next quite quickly. The bosses themselves are another exercise in recycling as they re-use a lot of mechanics from existing flashpoint fights; for example the last boss of Crimson Fang AoE-stuns the group to duel one person à la Malgus, and an earlier boss scans group members to summon specified "kill squads" similar to the way the Interrogator in Directive 7 chooses to clone people. Again, I didn't mind this too much because for the most part they have copied good boss fights, so why not? There's nothing to say that you're only ever allowed to use a mechanic once. I just wish the bosses had a bit more personality - just like the "story" of the uprisings, they are pretty generic. Even after several runs I struggled to remember any of them by name, with the exception of Crack-Shot Aggy from Done and Dusted (modelled after Colonel Daksh from Maelstrom Prison), and that might simply be because the name is short and easy to remember, and Done and Dusted happened to be the very first uprising I set foot into.
One thing I did like a lot were the small touches added for achievements that don't necessarily serve any purpose other than to have a bit of fun. For example in Done and Dusted you get the opportunity to summon a random desert beast to fight for you for a bit. While they make no real difference to the fight, it's plain fun to suddenly pull a bantha out of nowhere and to try to "collect" all the different animals. Crimson Fang and Inferno also feature friendly spies in hidden locations that grant you achievements for finding them.
Getting to this guy needed the help of a Gunslinger's roll and a Vanguard's Transpose. Not sure that's quite working as intended.
All that said, after completing both weeklies for this new game mode, I felt little inclination to go back to them for the rest of the week. If I want to play something fun- and fast-paced, I'm more likely to queue for a PvP match, which is less repetitive and also better for my Command XP bar from my personal experience so far. Maybe uprisings will fill a niche for a certain type of player that doesn't enjoy PvP, but I think that if I'm honest with myself I prefer my group PvE to be a bit longer and slower.
Oh, and you may be wondering why these currently don't have a solo mode, even though it sounded like there was one in the works at an earlier point in development. After seeing all the current uprisings for myself, I'm pretty sure that it has little to do with Bioware wanting to force people to group up and everything with the viability of the all-powerful Jesus droid that makes solo modes possible in the first place. There are a lot of mechanics like odd movement and target switching going on, which are not really that difficult but I strongly suspect that the GSI droid's current AI is simply not up for dealing with them effectively.