I would use any taxi company that charged me the price up front, paid through the app, calculated based on distance from source to destination and some heuristics about time-of-day, time-of-year, etc.
The driver would be incentivized to get you to your destination quickly and there wouldn't be that awkward tension about whether the guy is taking the best route, driving too slow or whatever.
Even if they occasionally lost money because of freak traffic conditions, I'll bet they would win over a lot of customers.
I feel like the discussions of what Uber does undervalue this. Medallion systems are silly, Uber is using some shady legal arguments, etc, fine. But the actual taxi experience is often terrible.
Last time I took an actual taxi in a new town, the driver spoke next to no English, misunderstood my destination, and got lost 3 times. He tried to drop me off in the middle of the woods because his outdated Garmin told him to. He then tried to charge me ~$80 because of all the bizarre detours, demanded cash instead of a credit card (at the end), and tried to follow me when I objected.
That's exceptional, yeah, but not hugely so. Uber's biggest value to me is the guarantee that the driver will have clear directions, not try to change route, take a credit card, and otherwise not scam me. The cab industry in a lot of places is really corrupt compared to other businesses.
It's not that exceptional, I've experienced that in several countries. Of course you could complain, but first you have to know who to contact at the local authority. With uber it's easy. If the driver tries to rip you off, you contact them and get fast and helpful support. And you won't have to pay if the driver decides to take a detour.
That's a common offering here in my home city by any company. You can ring them up and agree a price.
On the technology side... Gett.com seem to be offering an identical solution to Uber with the bonus of fixed price service within certain bounds. Looking at trips within a few miles of the city centre it'll offer a fixed price or "by the meter". Anything too far out however and it'll offer only "by the meter". Still, worth a punt?
EDIT: Bit more of a review...
I've contacted their support in the past and it's been pants. A couple of weeks for a human reply.
I also don't like how you have to decide the tip before the trip ends. Once you're dropped off, 'bing' the money is gone. I guess this is a culture difference but I prefer to decide to tip once I've decided I'm happy with the service. it's not a given.
Regular, real/official, taxi's are easily recognisable by their number plate which is orange with black letters whereas regular vehicles are white with black letters.
You don't have to use fake taxi's, that's your choice. A regular taxi ride in Stockholm and a Uber ride (depending on the time of day) usually don't have a big price difference between them. Unless you want to take one of the Tesla taxi's.
And taxis sometimes are cheaper than Uber here. I just moved apartments and paid 400 SEK for a taxi van to carry most of my boxes from one part of Stockholm to another, Uber XL was quoting a fare between 550 and 620 SEK.
I don't think that problem is unique to Stockholm, plenty of other cities have that issue.
Usually when I go to a new location, doing a Google search or two on these things proves helpful. The number plate stuff is on wikipedia and the VisitStockholm.com website for example: http://www.visitstockholm.com/en/Good-to-know/Getting-around... has all the information on taxi's, how to recognise them, what the regulations around them are and other methods of getting around.
A little bit of research upfront can spare you many unpleasant experiences no matter where you're going and regardless of if you know a local or not.
The issue is that there is no meter on the "fake" taxis. In other countries, you can easily tell if you're being ripped off based on the meter. If it's off, then you can be 100% certain.
I'd much rather use Uber.