This has been driving me crazy since I first installed OS 10. Mavericks. I've a bunch of Gmail accounts and none of them were working right in the Mac Mail app.
Apple is updated their Mac Mail app a couple times since Mavericks first released and to be honest it's still not working all that well for me. I've tried other mail applications on the Mac and none of them is as good as the Mac Mail app.
As far as I'm concerned they maybe prettier they maybe fancier but they just don't work is well for me. So I'm trying to make Mac Mail work. One trick I found online is to rebuild the mailbox. That is select the mailbox from the list on the left and then in the mailbox menu there is an option to rebuild mailbox that seems to work for me at least for awhile.
So give that a try to see if Mac Mail with Gmail doesn't work better.