If i do a card like Brain Control on my opponents monster that has equip cards equiped to it, when i gain control of his card the equip cards stay on his side of the field, but the monster still retains the effects of the equip cards right?

Yes, the Equip cards will stay on their field, and yes, the effects will remain active. But that doesn't necessarily mean the effects will work for you.

For example, if you steal your opponent's monster that's equipped with Big Bang Shot, and you attack their Defense Position monster, YOU will be the one who takes damage, not the opponent.

Thanks man, I just wanted to be sure cuz I was dueling my friend and he didn't believe me that the equips would stay on his side(cuz his s/t zone was full, so if the equips did switch he could use s/t's)

Just wanted to add, Trap Monsters (such as Stronghold the Moving Fortress or Embodiment of Apophis) WILL switch their m/t zone "holding" to you if you take control of it with Brain Control. So if you have 4 m/t on your field, you cannot use Brain Control, Snatch Steal, Enemy Controller, etc. from your hand on their Embodiment because at that point, you have all 5 m/t zones filled and there's no m/t zone left for Embodiment to put on hold.

Just figured it'd be useful to know, since it's sort of related.

but wouldn't brain control go to the grave after activation, thus you'd have a spot open for embodiment? oh well i'll keep that in mind too. Thanks ^.^

Cards do not go to the Graveyard until after the current chain (even if it's only one link, a.k.a., a single card/effect) has resolved, unless another effect purposely does so. So Brain Control doesn't go to the Graveyard until AFTER the selected monster is switched to your side of the field, which is why you can't use it on a Trap Monster if you have 4 m/t zones already occupied.