Both are valuable skills to have in your arsenal. If I had to pick just one, I'd say train more muay-thai, because it's more well rounded than traditional boxing... but every skill you learn brings it's own assets.
Please remember that range is fleeting in a street fight, the most often used tool is the hands / fists. Kicking range only appears very briefly, so kicks need to really count there - so Muay Thai would really work well in that range, if the muay thai fighter can recognise that and utilise it.
Remember most street fights start from within boxing range, so the fast, powerful hands of the boxer would be a better option in this range. The muay thai fighter could also use her hands, but remember, boxers generally have better hands. The muay thai fighter could also go for the clinch and chuck some knees and elbows. The boxer can also punch from the clinch.
My answer - they are both good, powerful martial arts that would be equally valid in a street fight.
It doesn't matter what the person trains in, it only matters how good of a fighter they are. For example, I would put Ali in his day against any Muay Thai fighter just because he could take anything an opponent could dish out, then give hit back to him five-fold.
Muay Thai is more exciting because you can kick use elbows & knees ! Boxing is a bit limited to only using your hands. I would do Muay Thai over Boxing
Always choose martial arts over boxing because in boxing it is where guys just try to punch the hell out of each other while martial arts is a more agile and complex sport (more fun too).
muai thai will be good if you practice it long enough, but boxing is easy enough to just learn and use, but again you are not going to be good in either sport if you don't practice