I've tried Nuevasync, Mailbox, and the Gmail app.....here are my experiences.
Nuevasync works as advertised, and since you keep your Mail app it's the easiest to use. The downside is that you have to have a separate account for EACH email address you have, and pay $30/yr for each email address you want push for. I have 7 email addresses, and want push email on 3 of them. It would be nice if they were able to process multiple emails for one Nuevasync account, and give you a MAJOR discount for multiple email accounts. Customer Service (very prompt responses) said their system was not set up for that.
Mailbox is free, works as advertised for push email for as many accounts as you want, and has some great extra features like Snoozing emails. The downside for me was that it only handles Gmail and iCloud accounts, and that you can't forward an email from a different account than the one that received it. Many of you may not care about this last one, but it's a big deal for me. Also, if you turn off your email address in the Mail app so you don't get email (and notifications) to both apps, that email address will be unavailable when needed by Safari.
The Gmail app works just fine for pushing gmail email accounts, but won't handle non-gmail accounts and does not have a unified Inbox. WTF. The last point is a deal-breaker for me.
For now I'm sticking with a combo of Mailbox and the Mail app. I have my 3 push gmail accounts using Mailbox, and I turned off all notifications for those 3 accounts in the Mail app. All my other accounts will just use the Mail app for everything. If I need to forward an email with a different email address I just open it up in Mail and forward it from there.