The sport of boxing overall is more competitive and widely practiced with a much richer history, but I think that's more because of Amateur boxing which has a deeper talent pool and more participants than professional boxing even does. As for professional boxing vs MMA which one is more competitive? I think it's debatable either way. Which is more difficult is relative to the individual and many different circumstances.
If you look at MMA, you find a lot of it's beauty in that people with lesser wrestling backgrounds or no wrestling backgrounds can manhandle and outgrapple Olympic wrestlers and National Champions. People with no striking background can outstrike and knockout Muay Thai, Kickboxing and Boxing champions. People with no black belt level jiu jitsu competition experience can submit elite black belt competitors. MMA is taking pure human combat and showing you what is really possible under the most open rule set, it's truly profound and beautiful at the higher levels.
As for the argument that you can't just "jump into boxing and become a world champion" well, no one ever just "jumped into MMA" and became a champion without at least a few years of training either. There's a fallacy in boxing that it's so elite and technical that you must train from a young child to have a chance at the higher levels. I will name you a large slew of boxers who reached the highest level within 2-5 years of training or crossed over in adulthood from Kickboxing to become world champions and Olympic champions.
Mike Tyson - Started Boxing at 15, by 19 was world champion
Vitali Klitchko - Crossed over from Kickboxing in his 20s
Marco Huck - Longest reigning Cruiserweight champ in boxing History, Crossed over from Kickboxing at 20
Deontay Wilder - Started Boxing at 20-21 years old, in 3 years was an Olympic Medalist
Sergio Martinez - Started Boxing at 22 years old, became all time great Middleweight
Dmitry Bivol - 8 fights into pro career, world champion
Bernard Hopkins - Began Boxing in his mid to late 20s, became an all time great
There's a lot more examples of this too, one reason why boxers don't become Champions after " jumping right into boxing " is because you need a marketable record, so they beat up 20 bums, go 20-0 and then challenge for a belt. It doesn't mean they weren't good enough when they were 7-0 however. That's a difference in Marketing/Culture often times moreso than a skill differential. Anyways it's debatable.