It's built on the SW3 engine, but with some tweaked movesets and also the extra characters from Z. The weapon system also was modified too. They use its main addition pretty well (switch between 4 characters in different positions of the map - also can give orders to the AI while you're controlling someone else) by giving a big focus to the objectives and zone control. Characters also have special skills that use the spirit bar and can have various effects, from healing yourself to increasing your army's power. Certain combinations of characters also have unique skills.
Although there's a big objective focus, the more annoying secondary objectives from SW3 mostly aren't there - like killing officers with a certain combo count and such. Unlike most Warriors games, there's only one mode, which is both the story mode and free mode (you can use any characters you've unlocked in any stage after clearing that part of the story), and you need to fight alongside certain characters and interact with them successfully to unlock their personal events and their moveset for the main character.
The main story is mostly linear and you can't chose factions during most of it. You fight alongside various factions in the first part, then Nobunaga in the second, Hideyoshi in the third, and only in the final one you get to choose between Mitsunari and later Yukimura or Ieyasu (there are also a few extra battle scenarios, that range from historical ones left out for some random reason to "dream matches"). Like mentioned before, you unlock interactive story scenes and events by raising bonds with each character and sometimes taking them to certain stages. So, everyone gets quite a few story scenes and interactions with the player, even if you can't really join their faction in the main plot.
They also include some battle dialogue for characters who aren't supposed to be in certain battles - like how Yoshimoto Imagawa has special dialogue if you take him to fight Nobunaga in the last battle of the first part. In fact, his story events take place after his death, somehow. Aside from the lack of side modes, another problem is the low number of grunts for a musou game though. Turning off the 3d adds more, but it's still a low number overall. Characters also had low detail models in battle, but they use high quality ones for the story scenes and conversations.
Anyway, I overall really liked it. The objective system + multiple characters work well, and then unlocking events and endings for the various characters was fun. Of course, if you can't stand the SW3 movesets, SWC likely won't be fun either. I just wish there had been more split paths before the final part of the story...