Thanks to my Mom for the idea for this post! This is not iOS 7 specific, and works in previous versions of iOS as well, both on iPhone and iPad.
When you setup a Gmail account in the iOS Mail Client you have the option for the default delete button to function as Gmail's Archive button, the default behavior, or Gmail's Trash button. This default can be changed in Settings > Mail, Contacts, & Calendars > Your Gmail Account > Account > Advanced. Change the default button action under "Move Discarded Messages Into:" to either "Deleted Mailbox" or "Archive Mailbox".
I've circled the button that will change depending on your selection, in a screenshot from the bottom of an open email. The icon shown is for archiving messages, while a trash can will appear to delete messages.
But what if you want to have a default, maybe Archive, and occasionally delete a message? No problem! Just press and hold on this button and you'll get options for either action.