May I ask what the problems have been with Supershuttle, specifically? I just booked them from LAX for our May trip (one way). It was quite easy to book online and the directions to find them at the airport seem straightforward. What have your issues been?
I've used them several of times, and the big issue for me was that you have no control over what order you are dropped off, with your fellow passengers, and it can be a serious drag on your time. The last time I took them from SNA, it took about 2 hours, because the van was full, some people weren't even going to the DLR area so we were toodling all over Fullerton, etc. and I was dropped off LAST. Also when they picked me up from the hotel on that trip, the 15 minute window was for like 3:15-3:30. I got back to the hotel to get my stuff out of the locker at 2:55, and the van was already there and the guy was mad and impatient that I wasn't there and ready 20 minutes early.
Also sometimes you don't take off from the airport promptly because they're trying to fill up the van. So you sit there or cruise around to different pickup areas before even leaving.
Uber, on the other hand, I booked ahead, and they were there and ready when we stepped out of baggage claim. The guy was super nice and friendly, and he cheerfully stopped at CVS for 5 minutes so DH could run in and get a rack of water. It was fast and door to door, and we didn't have to share with a bunch of strangers. The first trip we used the "first timer" discount codes that are always available, and the trip was free. From SNA, it usually costs around $22-25 before tip. Well worth it!
We're doing Uber from LAX this time.