This is isn't even a fair question....Kurt Angle
being a professional wrestler, and being really good, takes a unique combination of speaking ability and acting skill (mic skills), athleticism, and creativity. Brett Hart cant compare to Angle.
Angle on the Mic was so much better than Hart it isn't even close. As a fan fave or heel, deadly serious or cartoon funny, Angle can sell it on the mic. Brett managed to come up with a few crowd pleasing catch phases but he was one step above sleep aid on the mic. Having grown up watching Dusty Rhodes, Randy Savage, Jake Roberts, and probably THE greatest of all time Ric Flair, Brett Hart didn't have it. There were guys who were worse, but there were a lot of guys who were better.
Fact is Brett's lack of charisma was always holding him back. Vince was constantly searching for his replacement, from going with a heel champ in Yoko Zuna to pushing Hart underneath both HBK and Kevin Nash, Hart's inability to excel and sell it on the mic really hurt him. He was lucky he left WWE when he did because the promo crazy Attitude Era would have overwhelmed him between Austin, Rock, Foley, and HHH. John Cena is the Brett Hart of today, playing the hard working, kid friendly character to the hilt, but Cena is also way better on the mic than Hart.
In the ring both were very good. Brett sold believably and took a variety of falls, Angle was just as good, maybe a little better off the top rope. Hart had way more charisma, or at least knew how to maximize his image, in the ring than on the mic, but Angle matches were often mini events in themselves due to the hype machine surrounding the "Olympic Gold Medalist", and he always delivered. Angle gets this one by a slight margin.
Im not going to compare toughness....I know Angle wrestled with numerous injuries, but the fact is Hart was an iron man in terms of total matches for most of his main event run 1993-97, surpassing 200 plus matches per year regularly all over the world. You have to be pretty tough to do that. Hulk Hogan rarely wrestled more than a half dozen matches in a month in his prime, by comparison Hart was a machine. He wasn't quite as impressive as Flair topping 300-350 matches per year 1981-1985 but that was surreal. I give Angle credit for surviving the injuries but Hart gets credit for wrestling a grueling schedule and not missing much time.
Hart had a very good career, no one can dispute that. Fact is although WWE never seemed happy with him, constantly trying to replace him, they often went back to him because the Yokos, Sid Justice's, HBKs, and Nash's didn't bring in the revenue they wanted. Hart is often criticized for not being a big time draw, seeing as how he came after the period dominated by the likes of Flair, Hogan, and Savage, but Hart reached the top at a time the industry was fading and had been even when Hogan was still there on top in 1991. He also wasn't supported by a particularly strong undercard. If he was truly a bad draw WWE wouldn't have kept going back to him after experiments with so many of his contemporaries. I do feel his lack of charisma was contributing to his slide in 1997 and the advent of Austin & Rock would have been terrible for him, but he was the company's MVP 1993-1996. Angle may technically be considered a better draw but he spent less time as the focal point of the storylines as Hart did (although prominently featured) and he was supported by a much better cast with Austin, Rock, & Foley and latter HHH, HBK, Flair, & Taker. That's an element of star power Hart never had as a main eventer.
In the end, Angle is still the best over all wrestler. Great in the ring, great on the mic, convincingly playing good guys, tweeners, and villains, both as a serious character and as comical, Hart just cant compete. He was solid on the mic but nowhere near Angle's equal. In the ring it's too close to call but I think Angle was a tad better, more creative. Im going to call it a draw in terms of drawing power, based on the explanations of the previous paragraph. That scores well for Angle however, he's the best here. It's real....It's Damn Real!!!