There are technically three options. Having played every English FE game extensively, I'll explain them.
FE4-8 system. Weapon types are Swords, Lances, Axes, Bows, Light Magic, Dark Magic, Anima Magic, and Staves.
FE9-10 System. Weapon types are Swords, Lances, Axes, Bows, Light Magic, Dark Magic, Fire Magic, Thunder Magic, Wind Magic (The Anima triangle), and Staves. Note that FE9 lacked Dark Magic, for some reason.
FE11-13 system. Weapon types are Swords, Lances, Axes, Bows, Tomes, and Staves, and Dark Mages, Sorcerers, and characters with the Shadowgift can additionally use the Tomes Flux, Ruin, Nosferatu, Waste, Aversa's Night, Grima's Truth, and Goetia (provided they can use Tomes in the first place). Note that FE11 and 12 lacked Dark Magic entirely.
As you can see, by using FE13's system, we exclude an entire weapon type and thus an entire subset of classes (Light Magic), and gain effectively nothing, against FE7's system being more flexible with weapon types in general, allowing for much more versatility and a lot more class options. There's FE10's, I guess, but I can never remember the Anima Trinity of Magic in that game, much as I love the game, and further separating Anima complicates it a little too much in my opinion.