From what I have found personally, the wait times on Uber and Lyft are the exact same in my area in Canada. Every driver which is on Uber is also on Lyft. So I don't think the network effect is helping them much as riders aren't really getting anything different in terms of wait times. Also this is even after Lyft barely being about 1 year old in my city while Uber has been around for many years.
"Taxi apps" definitely have network effects from the two sided market, though not as strong as a social network.