I tried OpenEmu as suggested by vickerrrs. It started out with great promise. OpenEmu installs seamlessly - just download it and place the app in your Applications folder. Make sure you install the "Experimental" build or you will lack support for mame. (The regular OpenEmu build appears to emulate home consoles only.) OpenEmu even downloaded the mame "core" when it determined the core was not installed. OpenEmu starts right up and has a fully graphical interface. No more using the tab key to get to the game control mappings as in MAME OSX.
The area where OpenEmu fails to match MAME OSX is in the control mappings. MAME OSX allows you to map each of the arcade game's controls to your own controller. For me, that's a PS3 controller. OpenEmu only allows you to map the following: left, right, up, down, and buttons 1 through 6. The mappings you choose apply to all games. That works well enough for simple games like pac man or galaxian, which use a joystick and maybe a button or two, but arcade games that have complex controls might not be playable on OpenEmu. I tried crazy climber, which has two joysticks in the arcade version, and it just can't be played because the controls can't be mapped under OpenEmu. In fairness, most games have only one joystick and fewer than six buttons, so OpenEmu should be fine.
I found that more of my roms failed to play under OpenEmu than MAME OSX, after making the preferences correction identified by vickerrrs in an earlier post. I'm not sure why that is. The upshot is that I've gone back to MAME OSX. I haven't yet tried SDL MAME.