Soriku,
I'm a little late to the conversation and WoW already explained it perfectly, but you really should try Radiant Dawn (and preferably Path of Radiance before it). I'm halfway through it now and it's amazing.
The stories of these 2 FE's are very good. I like the GB FE's as well, but less.
What it comes down to is that the gameplay takes part on the battlefields, where you move each character in turn to perform an action (attack/heal/use item etc.).
After that the enemy does the same.
Big feature is that once a character dies he/she is gone forever, limiting the story and character development. (So normally you restart after someone dies).
After the battles the game consists of dialogues, story telling movies and the menu.
The menu is really extensive. You can watch extra dialogues that usually give you extra items or gain you party members, give skills and experience to characters and shop.
There are an enormous amount of weapons in the game, each with their own benefits. Some weapons for example are weaker but have higher chance of making a critical hit, others trigger 4x attack etc.
The main attraction for me is in the very deep strategy: In most battles you have a few characters that are very strong and can take most enemies out without any sweat. The problem is that these characters don't gain a lot of experience anymore, while the weaker units need it. It's a thin balance between attacking with your weaker units without endangering them. In the first part of RD there are units that die if attacked only once.
Sorry for the lots of double info, but I like this game (and series) so much that I wanted to share it anyway.
BTW: Volke rules.
