take someone on = challenge someone in some sort of contest. This is often used when somebody decides to take part in a match trying to defeat a strong opponent. It implies that it would be difficult to achieve but that the challenger is also of a reasonable standard and might have a chance:
I need a lot more practice before I could think about taking you on in tennis.
A variation of this can also be used when talking about tasks, implying that the task is somewhat burdensome.
I can't take on a new project right now because I haven't finished the current one.
take someone = (an informal phrase meaning) beat someone in a contest. This is probably more common when talking about future or imagined situations.
I think I could take you at chess. I've been playing a lot and you don't seem that good.
This isn't usually used about tasks in the same way as above.