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Here's the situation. I have 9 tyranid warriors which would make one big brood. But is it more effective to have 3 broods of 3 warriors than 1 brood of 9? or any other combinations?

It depends: Do you have the points to fill out the other HQ and Elite slots in your Force Organization Chart? If it's such a small game that you don't,then spread them out. If you do, then buy some other stuff.

For deathspitter units I'm a fan of 5-6 per unit.
in your case 4 & 5.

If your using them for synapse then larger broods can cover a large field, meaning your pretty much allways in range, however, in 3 smaller units you can spread them, allowing for more movement without worry.

for close combat - 6 - max sized units are great, more attacks from a good unit are allways better, by adding variety to thier layout you can also play about with wound allocation meaning you wont lose many warriors very quickly.

for shooting then a medium sized unit is good (1 heavy wep) and the rest standard layout work nicely.

however, if your playing KP then dont use small units of them, they are not hard to kill and will give away points very quickly unless your careful.

Only 1/3 of missions are KP missions.
Those that are, however, give a serious advantage to the 9 warrior brood.