Ha, another favorite scene of mine. I think this is what contributed to me becoming a Cap fan. In addition to that, I was starting to get into comic book message boards during this time. The message boards had tons of these match-up's with posters listing their encyclopedic knowledge of characters to prove their points. There were tons of Captain America vs. Batman or Captain America vs. Bane posts. Reading those, I realized how awesome Captain America was.
There were other media that contributed to me becoming a fan of many different characters. Marvel had published these huge coffee table books which were again readily available at Barnes and Nobles or Borders. I avidly consumed Peter Sanderson's
Marvel Universe book:
There were tons of articles in the book. There were tons of photos and illustrations as well. Poring over that, I began to appreciate tons of characters. It's how I learned more about Captain America and the Avengers. It was also when I first learned about Shang-Chi.
Also, I got a copy of Marvel Superheroes for Sega Saturn:
That was fun. It was great to play as Wolverine, Hulk, Iron Man, and Spider-Man. And again, that's when I first got to play as Captain America. All of those qualities that were in the comics, message board posts, and Peter Sanderson articles, like the super-soldier peak human abilities, the best hand to hand fighter in Marvel Universe, the ability to do all these crazy things with a shield, all of those things came to life in that video game. That's how I became a Cap fan.
So bringing it all back, the mid to late 90s was a seminal era for me. The Marvel/DC crossover TPB, coffee table books, message boards, and video games all played instrumental parts in becoming a fan of both DC and Marvel characters, especially Captain America.