Personal testimony as evidence:
I went to the Mall of America today to play some DK at one of the bars/arcade/bowling alley venues, and low and behold, the place had added a multicade to their stock! On it was DK, so I decided to play some (even though I had been intending on playing on their 3-in-1 cab), even though I'd have to use an 8-way, taller, fighter-style joystick. Due to the fact that we've been discussing this topic here, I messed around with cornering off of ladders as well as climbing while steering. I'd have to be honest and say that getting used to the different joystick was actually very easy for me, and that within just one game, the advantage of the 8-way joystick was absolutely apparent! It was like having an all new ability given to Jumpman. It was just as simple as having a small change in ability while climbing/getting off of ladders, but it was definitely a huge advantage (basically in many of the ways that have been mentioned) in terms of general gameplay. For anyone who is both 1) decent at DK, and 2) able to adapt and learn to play with an 8-way, there is absolutely no doubt in my mind now that it is a significant -if not, huge, advantage.
Take my personal testimony here how you will...