What are the differences with respect to battery life between using the regular Gmail setup as opposed to the Exchange setup?
I know that the Exchange allows for push, but is battery life affected much?
I have an IMAP and an Exchange email account on my iPhone 4S and when I only use Exchange my battery drains faster than when only using IMAP.
While I have configured IMAP to check for new email every 30 min, I must say I get lots of email in my Exchange account, that probably worsens the drainage.
Apple recommends here to "Turn off push mail", so it is a known fact.
How much is battery affected? I can't give you a number, it depens on many factors (how often data is fetched, number of emails you get, size of the emails you get) so just test it: disable Gmail IMAP, configure Gmail ActiveSync and compare.
After reading Michiel's answer below I was curious and googled "push vs. fetch iphone" and have seen quite a few debates. The outcome tended to be that using push conserves battery life, but some opinions just said "it depends".
My configuration is probably unbalanced and that's why Exchange uses more battery than IMAP (which is fetched every 30 min and not the 15 min as I posted in my original answer, now corrected). Please take this answer as my personal (non representative) experience.
In the link above Apple also recommends to "Fetch new data less frequently".
So again, test it and find out for yourself.
It's a matter of Push versus Fetch.
With Push (Exchange), the mail-server pushes new messages towards your device. While with Fetch (GMail), the device checks on the mail-server once in a while to check if there are new messages.
So, logically, Push uses much less battery then Fetch. Since your Fetch-device will check on the mail server every x-minutes. No matter if they are new messages or not.
Luckily, you can configure your GMail account as a Push account following these guidelines.