Brand specific, Big Red. Pretty sure it's regional, and the only place I can find it around where I live now is in glass bottles at Cracker Barrel. For flavors where I'm not picky about who makes it, vanilla soda, cherry soda, cherry vanilla soda, blackberry soda, and cream soda. Used to be really into grape sodas and root beer as a kid, but not so much these days.
Okay, tried Vanilla Nitro Pepsi This is distinctly better than it's regular flavored counterpart, which tastes like out-of-date RC Cola. This version has a nice, smooth flavor that evokes a cola-infused cream soda. Recommended.
That was my point---nitrogen isn't notably fancy or special, it's basically air. So how is this "special" pepsi?
Then it was a strange way to make a point. If you use oxygen or helium to infuse a soda, you're going to get a different result. But in your context, all of that is "air". I'd say the fizz is less heavy, resembling something closer to beer in texture than typical soda pop as a result of using nitrogen rather than typical carbonation.
1994 7up Ice Cola. It looked clear like 7up but with a very distinctive flavor. Of course, everything I like, they discontinue.
