So didi offers a couple of services: a taxi service, it just helps you hail a normal metered cab. I use that service every day, and it is no more expensive than doing it the old fashioned way...but during peak, I can input a tip (up to 20 kuai, or about $3), which helps me get a cab when I would otherwise not be able to. Call that "surge pricing" I guess.
The black car service, my wife uses that more. I have trouble using it since I can't epay (no chinese ID number to link to my unionpay card). But the cars are nice, the prices are a bit higher than taxis but we often get coupons that bring the price down. Still nowhere near to the cost of a taxi in the west.