Fiora used to be similar to Yasuo. A feast or famine champion that went 12/3 or 3/12. She was a boring one note champion. High damage, high mobility, no CC and no sustained duels. She was a glorified assassin that could barely make it work in top lane. When someone foolishly fed her a few times she could snowball her way to victory like nobodies business. If she made one mistake and died a few times early, she was a burden to her teammates.
Please do not ignore her glaring flaws. The reason people romanticize old Fiora is because of her ultimate, which wasn't all that good. Aesthetically it was very pleasing, but honestly it was just a point and click noob destroyer. After you reach a certain level in silver people would realize your deadly power came with QAAQAA, not the ultimate. They would build armor, and not feed you early understanding you fall off quite hard without early kills. Blade Waltz was mostly used as a finishing move or for lazy tower diving. It could be useful in small skirmishes, but deadly to activate in team fights because people don't group neatly and the moment you land you'd get locked down and burst into oblivion. People could even cancel her old ultimate as useless as it was.
The new Fiora is a dream come true as far as gameplay reworks go, and should be a model for future reworks involving champions that are feast or famine, including Yasuo. They managed to keep interesting parts of Fiora that we loved, but get rid of all the old clunky things that held her back. The new Fiora stresses timing and positioning, allowing you to make more interesting plays and be a bigger help to your teammate. Also let's not forget that she's actually a duelist now. She takes skill to use to her full potential, old Fiora was easy to pick up, but harder to play against people that knew she was a one trick pony.
When people argue about thematics on her ultimate it makes me laugh. I've been playing Fiora for years, and I like her ultimate. I don't really think that it should heal teammates as much as it does, but it fits her dueling style quite nicely and is a rewarding for besting her opponent which is very Fiora. She's a very showy type of character, and when the ultimate activates and heals everyone knows it's because of Fiora. A huge luminous Fiora rose over the battlefield declaring Fiora victorious.
The reason the "bring back the old Fiora" camp is so small is because she was a bronze stomper with little counterplay in soloqueue when she was fed. I remember when I first started how frustrating it was playing against a Fiora, especially if you made a silly mistake and fed her just a little. She got so out of control and the only way to shut her down was with a high amount of teamwork, which is asking for a lot when you're learning or playing casually. The other reason is because you couldn't get very far with her once you started facing people who used to be stomped out by her and learned how to play against her. Learning to play against a Fiora used to be one of the first steps to becoming a better player.