In my experience, and I have been in the auto repair industry for a long time and still run a mobile repair business, being mobile does not hurt the quality of a repair in any way. Certainly not because the work wasn't done on a lift inside a building. You can still get a bad mobile mechanic, but it won't be because the repair was done outdoors.
I'd actually say the finished job (certainly my own) is better than most of the same work done at a conventional shop, and I can say that because I've worked both ways. Mobile wins because you are one on one with one vehicle. Nobody is pushing you to finish and get the car out of the bay so the next one can come in.
Taking pride in the work
When I worked for someone else, if they caught me doing “unnecessary” things, like cleaning a valve cover until I could see the original paint color and putting it back on looking brand new, I got told not to waste time with that nonsense, they needed the bay. That's the culture in many (not all) shops.
I love it when a client opens the hood and can read the decals and see a shine on parts that were buried in grease and muck for years. I like it when every plastic clip I had to remove goes back on unbroken, because I took the extra time to release those little buggers carefully. I like everything to look like it was never worked on.
It starts with small things. Mechanics break clips (often it can't be avoided) but rarely replace them, so the wiring those clips held ends up dangling or resting against something hot, which shortens its life and looks ratty. Then it becomes leaving out the bolts that are hard to reach.
Working alone
A mobile mechanic usually works alone. I work alone. There's nobody to ask for advice on a difficult diagnosis, and that isn't a bad thing. You get used to it, and you build up an arsenal of reliable information sources, because without them you get a bad name fast.
Years of making decisions alone and staying dedicated to finding the real cause of a car's problem make a very intuitive mechanic. One or two bad mechanics in a shop with six good ones can keep making a mess, and the shop does damage control. A mobile mechanic can't take that chance. The job has to come out right, even if it costs him many unpaid hours on one car. If he doesn't diagnose problems quickly and correctly, he won't get the word-of-mouth this business runs on.
You keep your car
The biggest flexibility a mobile mechanic has is being able to look at your car, make a diagnosis, and tell you whether it's safe to keep driving. Drop a car at a busy shop for a warning light and it may sit for a day or two before anyone looks at it, and you don't have your car the whole time.
A mobile mechanic can see your warning light the same day and give you some peace of mind. Maybe it's a bad sensor that takes a day to get, with no ill effects in the meantime. I tell my client I'll be back on such and such a date, and meanwhile you still have your car.
You also get to see the work. You're home, so you can check on your car as often as you like, and you know how hard and how long the mechanic worked. That convenience is the holy grail of auto repair.
The hourly rate isn't the point
A mobile mechanic has low overhead, so he doesn't need to upsell you a bunch of trumped-up services (I don't). Most people looking for a new mechanic (and why are you looking, what happened with the last one?) decide on the hourly rate. One shop charges $85, another $95. I can't stress this enough: the hourly rate shouldn't decide it. A few dollars an hour barely moves the bill on a job of a few hours.
What you need to watch is the upsell. You bring a car in for a brake noise and they call to say you need front and rear pads, front and rear rotors, new calipers, hoses and a fluid flush. That's a red flag. It's not impossible, but it's not common. You probably needed pads, maybe front rotors, and the other $900 was pork.
Some people assume a mobile mechanic shouldn't charge a shop rate because his overhead is low. A mobile mechanic might do one or two jobs a day while a shop profits on twenty-five cars. He still has liability insurance, gas, truck upkeep, health insurance he pays himself, probably $50,000 or more in tools, and $800 a year in software updates. For some it's a side gig, and those are the ones missing the skills. For others, like me, it's the only thing I do. Judge a mechanic by what he tells you needs to be done, not by his hourly rate.