Behind Owen Hart and Chris Benoit, Brody has to be the most tragic story in wrestling history. Even more so because his murderer got off on a bullshit trial that ended before it began. Still I wouldn't say his death had much of an impact on his career as he had already carved out a nice niche for himself throughout 15 years in the business. His death shouldn't play a part in this decision.
Of the two, I'd have to say that Brody was more popular and influential than Kane all things considered. Brody may have never won a World title in any of the big three nationals promotions but he was one of the selling points wherever he wrestled. People did dish out their hard earned money to see Bruiser Brody take on guys like Abdullah the Butcher, Antonio Inoki, and Carlos Colon around the world. How many people have payed for a wrestling event strictly to see Kane? His influence on the business can be seen across multiple eras in guys like Luke Harper, Hacksaw Jim Duggan, and Mick Foley. To pro-wrestling, Brody was much more important than Kane.
On the other hand, Kane was a World Champion. He's been a main event talent for a good portion of his career, which has spanned nearly 25 years. I'd say Kane was the better talent in the ring and on the mic and much more versatile than Brody ever was. However Kane has also been known primarily for losing. His wins are not memorable and he was notorious for being the guy who jobbed to the Austins, Rock, and Takers of the AE, and the Angles, Cenas, and ...Takers of the RAE, and the Bryan's and Rollins of our current era. And I think if Kane were around during Brody's time, he'd do the job for him too. Kane's a good guy, Brody... wasn't at times.
If we're looking at longevity and accomplishments, Brody doesn't have enough to take this one, but if we're considering lasting influence, popularity, and international recognition, Brody wins every time. I put the latter above the former when it comes to someone like Kane and as such, I think Brody should take it.
Vote Bruiser.