50 years ago, karate had a big advantage. It was new, different and in minds of boxers in the boxing world, "street fighting with no rules".
At one of my 70's karate championship events, we staged a for real boxer (a former golden gloves champion) and a black belt (Walter Mattson) in a match. The boxer (Nev Kimbrell) could only use his hands since boxers didn't at that time kick. To make the event more real for the boxer, Nev wore 6 oz gloves.
The karate guy had a significant advantage and Walter knew how to keep away from Kimbrell and in the process scoring at will.
Fast forward to now. . .
With the UFC, the technical expertise and time training in all elements of fighting is the current "ultimate" in minimum-rule fighting. Boxers train as hard today but I doubt if any boxer could best a well trained UFC fighter in any match, with or without rules.
Now when I hear the question about "how will a uechi practitioner fare against a boxer", well you have a question with so many variables involved that it is a question that can't be answered.
How many uechi students train the way a boxer trains? How many boxers train when they reach the age of 40 - 50? Even for a couple hours a week?
I keep explaining to my students that most students who stay in the martial arts for many years, do so for many other reasons then to be the "baddest" ass on the block. If you really want to be a bad ass, sign up for a reputable mixed-martial art school. (But then, how many of these guys will be active and training when they are 70?)
If we are confident that our two classes a week qualifies us to fight against a well trained boxer or mixed martial artist who trains 5-6 five hour days a week, they should stop smoking that "wacky tobacci" and switch to fine scotch!