rush them really early, like within the first 2 minutes. they dont stand a chance.
for gdi vs nod, if your not very good at micro managing your attack force or just cant seem to get a rush going fast enough, just pump out predators and apcs. brutal ai will just about always building a few infantry to scout, then building 1 or 2 tanks before building a harvester. you can get your extra harvesters by building a refinery then selling it, you get 1500 back + a harvester. and 1500 is an extra tank + more
anyways, the key is to take them out before they can build up, if you go into a war of attrition against them, it does become rather hard unless you can micro manage very well.
however, if you do end up in a war of attrition against a brutal, just keep pumping out basic units like predators, apcs, riflemen and missile troops. make sure to rotate the damaged units back for repairs to maximize unit survivability. at the same time expand you base to new tib fields, and just spam harvesters on those fields. remember to harass the enemy harvester with your orcas, yes i know they are stealthed, but if you look at the tib field, you can see where they are harvesting so force attack the ground which the harvesters are on, it will still kill them. once you have a second tib field under control, start pumping out mammoth tanks from a new war factory (you really need like atleast 2 or 3 war factories to take on brutals in attrition). unit ratio shoudl be like 1 mammoth for every 2 predators and apcs you should only build if your having issues with air units or infantry. use the riflemen as both fodder and your anti infantry shield. obviously dont send the riflemen against black hands. missile troops make decent fodder too, but they can pack one hell of a punch if you make sure they arrive at the target at the same time. 100 rockets at once will kill anything in this game apart from a mothership.
anyways, they're just AI, can out smart them easily. if rushes dont work, just beat them using their own method of spamming units =]