service discovery, client-side or server-side?

Hey everyone, I'm trying to figure out service discovery for my microservices. We've got a few ways to go about it, like client-side discovery (think Eureka client) and server-side discovery (using a load balancer and a service registry). What have you guys found works best? Is one way way simpler to handle or faster in the real world? I'm really interested in the downsides you've run into.