I know I won't be able to remember everything Brooke and Erica have done to each other over the years, but...Basically, Erica and Brooke have vied for the same guys a lot over the years. Yes, they were both married to Tom Cudahey at one time or the other (Tom divorced Erica because she was taking 'the pill' while telling him she wanted to have a baby with him, Tom and Brooke had a child together who died in a accident, a car accident I think). They were both married to Adam. As far as I remember, Erica was never romantically involved with Tad, but Brooke was. And Jack and Dimitri were factored in there too, I think. Maybe not Dimitri, I'm probably thinking of Edmund.
Basically, Erica has told Brooke on many occasions that Brooke can only attract Erica's discards, which has never sat well with Ms. English. If I remember correctly, Brooke has always been involved with someone after Erica (Tom, Adam, Jack).
Erica was the rich and powerful 'wanna be', Brooke was the real thing via her Aunt Phoebe. Bad blood between them forever.
I've probably forgotten some of the reasons they dislike each other so much. Maybe someone else will pop in and fill in some of the blanks.
~kath