Been using the Boxer email client on the iPad for a week now and recommend it as a replacement to using the standard email client that comes with iOS.

These are what I think you will like.
– Works well with both Outlook and Gmail
– can create folders that connect across you different accounts
– you can make the swipe to the left and right work for you
– you can make it default to using Chrome as the default browser
– seamless integration with Evernote
– it remembers where you are filing emails so you don’t need to spend time saving emails into folder is quick.
– it looks great

Things that could make it great
– At the moment you can’t view a message full screen without clicking reply, this is annoying.
– if you set it up on other devices all your preferences and account setting could come along with them
– Being able to file messages from one email account into another accounts folders
– opening attachments can be problematic at times.

UPDATE:  I had to delete the program from my ipad as the Syncing with Outlook was just too unreliable so was unable to use as my daily client.