For one thing, how many drivers they have matters. More data might produce better estimated ETA (at least Uber use the data from the drivers to predict future traffic congestion, etc.).

Another thing is how well they control supply and demand. Say Uber has 10x drivers than Lyft, what if Uber has 100x consumers than Lyft? Uber likely has to surge at a very high rate, and the consumer can't afford a surge might go to Lyft instead. Since Uber can't control well how many total consumers they have at the moment without surging, one realistic alternative is to just reduce the number of Lyft drivers, so Lyft have to charge higher rates as well.

Here Uber doesn't just want more consumers coming in, because even less consumers is better than more consumers come in initially and can't afford a surge and then have to turn to Lyft.

So to sum up, in the end, Uber have to recruit more drivers (hey, they even just opened API for their product) or cut the number of drivers from Lyft (through alluring them). You can't blame Uber on that, it's the competitiveness of this market.