"Boxing vs Muay Thai" is very popular subject on many martial arts forums. I would rather focus more on pointing out how you can you combine those two styles for your benefit. Why? In my opinion Muay Thai and Boxing are a complementary fighting styles and mixing them will help you to become a more complete fighter. Thai Boxing practised in Europe is greatly influenced by Western Boxing these days and it made it even more effective. Let me explain my point of view.
Traditional Thai Boxer would have an advantage when fighting on long distance thanks to a various types of kicks, but would be hammered within arm's reach distance. The advantage of elbow strikes and clinch game would be diminished since boxer would likely keep a medium range and attack with a combination of a powerful punches.
However, since Muay Thai evolved greatly under influence of western fighters and incorporated Western Boxing strikes, same fight would look quite different with a modern Thai fighter. Good boxing skills and versatile Muay Thai strikes would let him to dominate in the ring. Some K1 fighters, like Mike Zambidis and Joseph Valtellini even use boxing as their main weapon adding up some kick and knee strikes in the process. You could argue that this is not a traditional Thai Boxing, more like a hybrid style. And you would be correct but without it MT just wouldn't be so effective. That is what's really great about Muay Thai - it keeps evolving while keeping those parts that make it very distinct.
Modern Muay Thai, especially the version practised by foreign Thai fighters adopted and developed some useful techniques from Boxing and became even more effective martial art. Watch the fight between Joseph "Bazooka Joe" Valtellini and Alex Berrios to know what I mean. Pay attention to Valtellini setting up a pace for this fight with his boxing skills. It shows the advantage of an enhanced Muay Thai over a more traditional style. That said, I highly recommend learning both of the styles and then switching them when needed.
My point is: traditional Thai boxer without Western boxing skills would struggle with a good professional boxer. Modern Nak Muay with developed proper boxing skills, would have an advantage over traditional boxer thanks to his distinct Thai boxing skills.
But remember, with more techniques to use comes a higher learning curve. It takes more time to master them all and to become a pro fighter.
Also read Muay Thai versus other martial arts (Karate, Kung Fu, Capoeira and more) post.
Muay Thai vs
Boxing vs Muay Thai