I doubt there's a huge difference in battery consumption either way, but the exact impact really depends on your specific usage patterns. Read here for a discussion of the battery impacts of push email vs. scheduled syncs:
http://forums.androidcentral.com/sam...ips-myths.html
As far as "which is better," it's really up to you. Some people prefer to use one app for everything, and get all their emails combined into one inbox. Some people prefer to use one app, but keep the emails separated by account. And some find it advantageous to use an app that's optimized for each email account (e.g., the yahoo app, the Outlook app, Gmail, etc.). All of these approaches work, so it's really what you feel works best
for you.
My primary personal email comes in through Google, and I use the gmail app for that, which is push email. My primary work email is Microsoft Exchange, and I set that up using the main Mail app. I set it for push email when I'm out of the office, but (if I remember), set to sync only once an hour when I'm at my desk. Also only once an hour outside of work hours. That saves battery when I'm getting a lot of emails. My secondary personal account, used for commercial accounts mostly, is a Yahoo account. I don't really use it enough that I need to check it all the time, so I use the default mail app for it, set to 1 hour sync during the day ,and no sync late at night, when I'm sleeping.
