That is a trade off with some pretty deep implications and some subtleties. I doubt it's such an obvious choice.

I've been thinking about pushing more in my client make less work for my servers.

Evaluating map data inaccuracy? More than just a payment UI? Driver/passenger matching? Data analytics? (Doesn't that require information from multiple clients?) On the client?

I mean, you could push some of that to the client, but I'd understand why your app is gigantic and doesn't do app-ly job very well with all the background processing. And I'd be surprised the app hasn't been hacked to get at the analytics data, if not the payments.