I think that boxing and karate punches are both good depending on the situation you're in, and I train both.

In Aikido class when it is my turn to be Nage I stand, knees slightly flexed, with my arms and hands hanging relaxed. That way I can see Uke's feet and can judge when where and how he will attack. Sensei has never corrected me on it.

The so called 'boxing punch' is, and has always been, part of the karate curriculum. (E.g. mawashi-zuki, ura-age-zuki, kizami-zuki.)
The only reason I can think of why the focus of training in most karate schools is on the choku-zuki/straight punch, is because it is the most unnatural of the two types described by the OP. By unnatural I mean, it is a motion that doesn't come natural to most people, and thus needs the most attention in training.

Maybe the best way to differentiate between the 'karate' and 'boxing' punch is based on the mechanics; the first being a delivery method of force from the hip (+ lower shoulder muscles), the later being a delivery method more from the upper shoulder.
They certainly aren't differentiated based on the guard (position of execution), since that isn't static. It's up to the fighter, what they find suitable at the moment, what kind of guard they keep.
(At least not in my book.)