The longer grip on the Service model is a bit harder to conceal, it has a tendancy to print with the end of the grip. The compact solves this by making the grip shorter...and thus less likely to print.
However, there are people out there that can conceal just about anything.
Much of it depends on your size, weight, and build.
You really need to go get your hands on both of them and try out some concealment options to find what works for you.