Story: Using the 5 Elements of Story method, comparing FE7 with FE9, here's the simple answers - FE9 easily has better worldbuilding and better themes, there's no competition in that area. FE7, however, has the better plot. I think I mentioned this before, but FE9 really drags in the Bengnion/Serenes sections, and the opening missions feel isolated from the story (bandit trouble and little else). FE7, on the other hand, can broadly be divided into three sections (Lyn's story, Eliwood's story up to losing his father, then the rest of the story up to the point where Eliwood and co. finally return to Valor. Also, FE9 plays most of its cards at the start, whereas FE7 starts off with a girl just trying to find her grandfather, and ends with a showdown centuries in the making against Nergal, who while not the deepest villain in the world, is still a more interesting one than Ashnard.
So that leaves characters. This is a weird one. FE7 has an extremely strong core trio (Eliwood, Lyn, Hector), plus a no. of close supporting characters (e.g. Ninian and Nils), and a massive gulf between them and every other member of your party bar a few exceptions (e.g. Nino and Jaffar). FE9, on the other hand, has a weaker core cast (Ike's good, so are the Greil Mercenaries, but not great, and Elincia's a doormat through most of the story), but on the other, almost every single playable character in the game has some level of memorability to them, helped in large part by base/info conversations, and how much easier supports are. At the end of the day, I'm going to call characters a tie - FE7 has a stronger core cast but weaker supporting cast, while FE9 is the opposite, with the line between 'core' and 'supporting' blurred.
So that leaves storytelling. Really, there's not much to contrast here - both games tell their stories using the same method FE always has, with static characters in place of backgrounds. FE9 has cinematics, but they're terrible, so there's not much to say there. FE7 has the benefit of gaiden chapters, while FE10 has the benefit of shifting backgrounds, adding more to a sense of place, not to mention the ease of support and info conversations. Overall, I'm going to give this to FE9 but really, the difference is so minor, it's barely worth counting up.
So, yeah. In terms of clear wins, FE10 has better themes and worldbuilding, FE7 has better plot, characters are a tie, FE9 has better storytelling, but it barely counts as a difference. So, FE9 should win, right? Well, maybe, but the difference is that not all elements of story are equal - something like plot is far more important than theme, for instance. I guess at the end of the day, I like the story of FE7 more, but on an objective level, I think FE9 is superior. Bear in mind that FE7 has the nostalgia factor, so if I'd played FE9 first, what then?
Overall, FE9 wins in story. So what about gameplay?
This is also hard to discuss, in part because I don't have a paradigm I can fall back on for gameplay. That, and it's easier for me to talk about story rather than gameplay anyway. But I'll try:
FE9 Pros: Great mechanics (e.g. cavalry, laguz units), decent addition of the bonus XP system, plus the talent system, plus the easier supports
FE9 Cons: Game is far too easy, has limited replay value
FE7 Pros: Gaiden chapters, greater replayability, the magic triangle (in addition to the weapons triangle), handles difficulty excellently
FE7 Cons: In light of POR, FE7's support system is terrible, cavalry is less interesting to use, etc.
I guess the difference is that in moment-to-moment mechanics, FE9 wins, while in replayability and overall feeling, FE7 wins. Really, I'm just going to call gameplay a tie. Each game does certain things better/worse than the other.
So, how do the games stack up? Well, to rank the FE games I've played to any meaningful extent:
6: Heroes
5: Shadow Dragon
4: The Binding Blade
3: The Sacred Stones
2: The Blazing Blade
1: Path of Radiance
Yes, as agaonizing as it is for me to say, I think PoR earns the top spot. Being as objective as possible, it just doesn't feel right to call FE7 the superior game, no matter how much attachment I have to it. As another litmus test, if someone was asking which of the above 6 FE games to start out with, regardless of any consideration of actually gaining access to them, FE9 would easily be the one I recommend.
So, yeah. That was fun.