I remember Chelsea taking the Holgate End back in the 70's, but have no idea which season it was. The only time I ever saw a Boro mob at the Bridge was the play-off game, and they were very lucky there was a fence to protect them. Having said that, Boro had a half-decent mob, though they did tend to throw darts at away fans which was pretty cowardly in my opinion.
We've never really had a rivalry with them though, not sure how a southern team can have a rivalry with a northern one. Apart from West Ham & the Geordies, but that was based on one incident involving a petrol bomb. Our rivals have always been Tottenham and West Ham, and to a lesser extent, Arsenal. QPR and Fulham like to think they're our rivals, but that's a bit like Hartlepool or York City claiming to be Boro's rivals