I'm now quite a distance into FF2 (not FF4). I had an unfair prejudice against this game in the past, and never gave it a fair shot.
First, the game feels much more modern than FF1. The battle system, should you choose not to abuse it, is well balanced and quite a lot of fun. The game is basically a workout routine - use magic and you gain MP and magic power instead of xp. It's basically an AP system, except your AP is automatically assigned based on your actions rather than manually assigned. It's otherwise the same as the SaGa systems. I find myself using magic frequently, almost all the time. It never feels like spell usage or weapon experimentation is a waste, because the more you use magic, the more you power up the spell, and the more MP you gain - and weapons that haven't been used advance quickly in the later game, I started a character in swords for the first time, and she gained about 5 levels in about 7-10 battles - everyone else is at level 11 right now, she's on level 6. That's without any boosting cheats on. So far the only cheats I've used are No Encounter, when I run out of time and want to get to a good place to stop - unfortunately, in early open world games, if you leave off at certain locations, sometimes putting the game down for a bit means forgetting what you're supposed to be doing (actually, this has never happened to me, but I imagine it could easily happen if I'm not careful).
Story is quite good for an NES game. It's not Dragon Warrior 4 good, it probably falls between Dragon Warrior 2 and 3. Definitely a better story than FF3 (again, the NES game) if my memory serves. It's your typical Sakaguchi "The unlikely hero who joins the rebels against the Empire" story with very good and evil characters, and one who is not sure if he wants to be good or evil. FF6 may have started with that Sakaguchi concept, but the new writers under Kitase took the story in a very different direction and did away with the idea of a singular main character, and made the story much more about magic, Espers, with some steam and science fiction elements, big theological concepts, and everything eventually ends up in a war on a god story in a post apocalyptic world. But, otherwise, the story is impressive compared to what I thought it would be.
The dungeon design is kind of annoying with a lot of empty dead ends, this is something largely done away with in the era of Final Fantasy Adventure, FF3, and Final Fantasy Legend. That said, the dungeon design is less annoying thanks to auto-battle and the ability to turn random encounters off if you're thinking "You know what? I just wanna finish this dungeon." But, I'd recommend not doing this too often as sometimes there are spikes in regular enemy difficulty. But if you wanted to just get things over with, put your battles on for one floor with 4X yields, and then turn it off for the next three dungeon floors. Although, I like the dungeons more than FF1.
The world is substantially better than FF1's world. There are houses you can go inside to visit people in the towns - FF1 didn't have this. It all feels a lot more modern. FF1 had some caves and castles to go inside, but towns were purely shops, anyone who could be talked to in a town was outside. Additionally, the people say more interesting things, FF1 felt so soulless in terms of what people said. FF2 they say things much more relevant to the current situation, and text evolves over time, probably better than FF4 (if I correctly recall), maybe even the best until FF8 (where dialogue from non-player-characters frequently changed over time, especially in Garden). You can also ask characters about different things from a list of terms you gather (similar to Shadowrun on SNES), but unlike Shadowrun, it highlights all the terms the characters have something to say about, Shadowrun, you basically had to go over the full list with everyone in the game or you'd probably miss something important. So, the world is a strong point for this game, it is a massive improvement over FF1. Also, I really dig the more open world feel to it, even though in reality the story is still linear.
Side note - Romancing SaGa 2 is more authentically open world in gameplay, although (unlike FF2) you don't have access immediately, you expand the world over time, and expand the number of available paths to take.
Overall, I like FF2 more than FF1. In terms of the remasters, I'd say I like FF2 two to three times as much as FF1. I'm exploring the final continent now, so I think I'm just about done.
MAJOR TIP - whichever character you plan to give ultima to, make sure they’re learning all weapons and a wide variety of spells (I like attack spells and common heal spells, especially cure and life that increases points if used outside battle. Ultima’s power is based on a combined count of all skill levels a character has, so if you’re really good in swords and nothing else, Ultima won’t be anymore powerful than a fire spell. Note, I had all weapon classes up to level 8-11, and all magic between level 6 and 16 (the level 16 spell being Cure, the easiest one to level up). Ultima was by far the most powerful spell in the game with these stats.
The last dungeon was brutal because of the length. It was basically like FF4's final dungeon, except not fun (because of all the dead ends). By the end of the game I was just using Ultima all over the place. The final boss wasn't particularly difficult. In fact, I had much more trouble reaching the end boss than actually fighting him. The game is roughly 50% longer than FF1. Weird enough, FF1 and 2 both took me longer than my last playthrough of FF4 (which was about 9 hours), FF6 I can do in about 14 hours, but comfortably (talking to everyone) is more like 20. FF1 is about 10 hours, FF2 about 15 hours.