So, I'm a low platinum Zerg player at NA, and as a Zerg player I'm extremly confident on my ZvTs. doesn't matter what they do, they just don't seem to do it right - because I almost always am able to defend it, given proper scout.
My ZvT style is probably very similar to IdrA's and most of the zergs out there: massive amount of mutas, close to zero units besides about 80 drones. The terrans I play against always end up wasting tons of money on turrets/thors and I just overwhelm him with lings later thanks to map control. Should a counter attack comes, I have no problem microing my mutas to desroy his tanks or medivacs while sending in banelings.
My ZvP style is my worst tho, I do the usual roach/hydra mix with corruptors as needed, but I never feel I'm well with it. I've tried mutas as well, dealing a lot of eco damage, but they just don't seem to finish their job well enough. Still researching.
However, I just discovered my ZvZ style. I hate ZvZ out of all matchups, simply because it is such a weird matchup. What I am doing atm is either 14 hatch or 15gas/14pool->FE all day long. Then I get a quick roach warren and make roaches out of one gas, the rest spent on drones - copied from Day9's Daily on IdrA actually - and then switching into pure roach/hydra out of 4 gas, with one evo chamber going on. It has proved to me to be very effective as my hydras are usually well timed to any mutas, and I'm able to deal with most early rushes. I haven't played against a solid macro player however.
Speaking of macro, recently I played a have where my oponent opened with a faster hatchery, and I went 15gas/14pool. Obviously I couldn't do enough damage to it, but I ended up getting the upper hand thanks to better macro, or so I thought. I went for an attack as he failed to send a ton of lings into my base, and my roaches completly destroyed his natural. Suddenly, about 12 to 15 mutas pop in my roaches - thank god I had a hydra den ready already - and I continue to struggle to get a third since the guy is just so good at mutas.
I get then infestors, obviously, and roll some of his mutas and proceed to attack his natural again with tons of roach/hydra. The guy made banelings. BANELINGS. And fungaled my army so perfectly, that my hydras were gonners. And then, the mutas. OOOOOh the pain of the mutas.
I never thought that mutaling would actually work in a ZvZ, but hell I was wrong. He then proceeds to attack my 4th(gold) attempt, and I'm like "fml I'm dead". In a very lucky reaction(or just pure instinct?) I hit the money fungal that traps about 20 mutas to my hydras to roll. He looks at that and just says "wp". I was having nerdgasms.
Then I just win the game - turns out the guy tried to go ultras as I was taking my hive(for +3/+3). Shame, BroodLords would be so mure more effective with his micro IMO. Still won, really cool game.
I'm still trying to find out my ZvP style, anyone care to post cool styles for ZvP? Well, altho I first need to survive the freaking 4 warpgates...