For one, there were usually an incredible amount of enemies chasing after you that you must fend off along with a number of enemies guarding the area of your escape. These missions contained a red arrow that you must get Prince Leaf to in order to win. The first was escape missions, and they contributed to the immense difficulty of Thracia 776. Of course, the seize missions made up the vast majority of the missions in the game, but three new types of missions were thrown into the mix. The most important thing it added was new missions instead of the usual seize the throne/castle missions.
The personal skills of Genealogy return in a tweaked form, but Thracia 776 added a lot more to the gameplay of the Fire Emblem series.
The game is full of cameos and spoilers from Genealogy of the Holy War, and you probably wouldn't even understand a lot of it because of that. If you are interested in playing the Fire Emblem games you should not even think of playing this game before Genealogy. Thracia 776 also overlaps a little with chapter seven of Genealogy, and ends where chapter eight of that game begins.
The game takes place between chapters five and six of Genealogy of the Holy War, and contains so many spoilers of that game that there isn't much that can be said about the story of Thracia 776 without spoiling Genealogy of the Holy War. Thracia 776 takes place on the same continent as Genealogy of the Holy War, Jugdral, and in it Prince Leaf of the kingdom of Lenstar attempts to protect his kingdom from the invading forces of Thracia. This doesn't mean the game was bad, however, it was just released at the wrong time and on the wrong console. However, this didn't lead to great sales of Thracia 776 so the game was released as a standard Super Famicom cartridge in January of 2000, giving it the distinction of being the last Super Famicom game to be released, but also the dishonor of being the worst selling Fire Emblem game. These catridges, known as Super Famicom Nintendo Power carts, allowed Nintendo to continue selling Super Famicom games long after production of Super Famicom cartridges ended, and the program was in place until late 2002. The few games that wouldn't work with this system were those with special chips in the cartridges such as Star Fox and Super Mario World 2.
Nintendo had started a system that allowed gamers to buy blank Super Famicom cartridges, which they could use at Lawson stores in Japan to download almost any Super Famicom game. Nintendo didn't release the game on a standard Super Famicom cartridge, however. For some reason Nintendo decided to release Fire Emblem: Thracia 776 for Super Famicom instead of Nintendo 64 in September of 1999. Genealogy of the Holy War was released in the same year as the Nintendo 64 so most people assumed the next Fire Emblem would be a Nintendo 64 game.