Nowadays GMail is one of the most popular e-mail clients for the general public and most of us do prefer to use multiple mail account to just keep the work and personal mails separate. If you are using your iPhone and want to check these two (or more than 2) all the time, then I have few tips which might help you to do that with a greater ease.
Use Safari for the other account.
Now this method is relevant if you are using only 2 GMail account and you want only 1 GMail account in your default iOS e-Mail client. You can configure a GMail by selecting this option in the Mail account.
So this way you can use 2 accounts simultaneously.
Use Multiple GMail account in iOS Mail client.
Another very common method is to add various accounts of GMail on your default iOS e-mail client. You can manage multiple accounts by selecting the options mentioned in the previous step. The only problem you might face is unable to read the offline (new) chats (in your inbox) or any type of chat history.
Finally Use Gmail app for iPhone
As already mentioned in my previous post related to the new GMail app, you can add multiple accounts in this application and it will also you to check all the chats in the account. It takes more time to load the new mails as compared to your iOS Mailbox.
I have used all these steps but the last one is the most convenient, it will show you all the chats and have a better UI as compared to the default iOS mailbox. For faster syncing of mail, I would say that you should go for the second step. In all, the last step is the best and I hope this help you. Please let us know if you face any problem.