I've heard that Lyft is a bit cheaper than Uber, but I haven't tried it out. Uber is built right into Google Maps, which makes it so easy to use that I'm too lazy to try anything else.
I've met many drivers who do both simultaneously. When an Uber fare pops up they disable Lyft and vice versa. That way they're almost constantly taking fares.
I find Lyft to be cheaper but Uber more frequently available. One thing Uber does to keep up with supply and demand is Surge pricing, where they increase the cost to X times the normal fare. Usually 2-3 times. I believe Lyft does the same, but theirs is always a flat 1.5x or something. Earlier this year when roads were iced Uber surge pricing got up to 7.6x rate. Would have taken over $100 for a short trip. Pulled up Lyft instead and only paid like $20, just tipped the guy a large amount which I rarely do for these rides.
Capital One QuickSilver card is offering a year long promo with 20% back on all Uber fares as a end of month statement credit. Pretty decent deal for people who use it often.