I've used the Gmail app, but always return to the native mail app for my Gmail account. Simply put, the native mail app is sufficient for my use. As for Hotmail/Outlook, the native mail app works well and sync well with my device. Still, to answer your question, there are several third-party apps that work well with either.
I have tried the gmail app, and I come back to the native email client because it is so well integrated with everything. One thing the gmail app does very well, though, is instant notification of emails. If you use gmail and you want to get push notifications instantly when you get an email, the gmail app is the only way to do it.
I'm accustomed to having my 3 emails separate from each other while using android and WP. I'm going to try using the gmail app for gmail, cloudmagic for outlook and the native app for my work exchange email.