I agree the spitting is much, much worse. That is a totally unacceptable behavior and requires a punishment. If bragging was happening, it was rude, but spitting is a physical assault. As for punishment you always have to find their "currency." With my 14 year old it is the phone or the computer. With my 10 year old it is video games and TV. You have to find what they really like and take it away. OP said it was play dates or friends, if she had a play date scheduled I would cancel it and tell her it was cancelled because of her actions, or I would tell her she has to stat "in" until Monday, if she likes to play with friends after school.
As for the bragging, if the conversation wasn't heard, who was it that said she was bragging? If the spitter said it was bragging, it may have been that the spittee was excited and talking about it and the spitter, who was jealous, interpreted it as bragging. ....or she may have been bragging, knowing it would get under her sister's skin.
Either way, I agree with you OP, the spitting is a much bigger offense than the bragging.