수고 많았어요 and 고생했어요 The two phrases are very close in meaning. The difference is that 수고 is used more widely and to acknowledge any type of endeavor including even routine work, while 고생 tends to be used more about doing something special or unexpected. So 수고했어요/수고하셨어요 and 수고 많았어요/많으셨어요 are said almost like a greeting (like "I appreciate it"), to one's subordinates or colleagues at a workplace (to one's superiors or elders, these may not be the best way to say it). 고생했어요/고생하셨어요 and 고생 많았어요/많으셨어요 would be more appropriate if someone had a particularly difficult time doing something at workplace, or if someone who's not normally doing such kind of work volunteered and took care of it. But the difference is small, and they are often interchangeable.

수고많았어요 = 고생했어요