I'd say do both or like Thaison says find a good muay thai gym. You could be lucky enough to have a good muay thai gym near you where the coach also has a traditional boxing background, this is not unusual. Boxing will make you good with your hands and teach you the importance of head movement among other things. Muay thai will teach you how to throw and defend against not only kicks but knees, elbows and will teach you useful techniques for controlling your opponent in the clinch. All things that boxing won't even touch on.

I went along to a boxing club a while back after doing many years of muay thai with a a coach who was a good amateur boxer. I found it very difficult. I found it very hard to alter my stance for boxing and felt crippled without being able to use my kicks. I'm 6' with long legs so I always preferred to kick. Needless to say, the boxers destroyed me when sparring.