Which is better, a dog or a cat?
Lattice brace instruments tend to have thinner tops. They TEND to be louder, have a stronger "attack" and less sustain. There is a lot of variation though, from what I understand. Smallman guitars have a very thin top, and the structure of the top is kinda weird. Smallmans are known for their loud, almost percussive tone (some liken it to a banjo, but I disagree.... John Williams plays a Smallman and I like the tone he gets out of it). The Cordoba C12, though lattice braced, is not constructed like a Smallman type guitar. The top is thicker, probably closer to the dimensions of a fan braced instrument, but braced differently.
From what I've heard and seen on youtube, and the Cordoba website, the C12 is pretty loud, a little on the punchy side, but still seems to have some nice sustain.
Fan-braced instruments have a series of braces radiating from just behind the bridge toward the lower bout of the instrument. This is the more traditional style of construction popularized by Antonio Torres, and is used in most classical guitars on the market today, especially factory instruments such as the GC32. Because there are many different variations of fan bracing, it is hard to generalize other than that they are supposed to have better sustain, a little less volume, and a less aggressive attack compared to fan braced instruments. The choice of top-wood (Spruce vs. Cedar) will also determine tonal qualities (Cedar: darker, punchier, more colorful... Spruce: brighter, cleaner, sweeter, ,more sustain), although these are also generalizations.
Again, these are all generalizations. David Jaggs offers some videos for download on Tone production for the Classical Guitar, the second video of which discusses differences in construction styles, materials, and their effects on the tone of guitars. You pay a few bucks for the download, but it's worth it. If you look around, you can also find other videos talking about construction of the classical guitar.
In the end, the proof is in the playing.