In WoL, Terran had to constantly drop, attack, kill hatcheries, kill tech from Zerg, all while trying to get new bases, defend from muta harass, etc. Whereas now in HoTS, Zerg can't just win a bunch of battles or sit back in there base. Think real far back to game 4 of Bly vs. Flash in the first MLG HoTS tourney, Bly wins every engagement but is killed by Flash's economic harass. Also, the entire Leenock vs. Innovation series there; Leenock is defending extremely well, but gets barrel stomped by Innovation because he never attacks the Terran; he's just winning engagements.
This sort of brings a new light to this game for Zerg that I feel only the high level Terrans have seen and incorporate into their play (Polt, Innovation, Flash, Maru, Bomber, and Mvp way back when): just like in chess, you can't only think of the game in terms of pure material advantages, but also in terms of what the advantages mean. For example, I can sacrifice a queen to you, but in exchange I could be dishing you a checkmate (because the queen's death could be in some random corner of the board far away from where the piece in question should be that could've saved the King if it were in its original place). In the same way, Zerg can no longer sit back and auto win because they teched to Broodlords and a-move from there; with the improved mobility of Terran army compositions (mines are significantly faster than tanks to be placed), Terran army compositions, with improved control, seem almost like a ranged version of ling/bling; the sheer number that can be produced by Terran can actually begin to rival Zerg's with even perfect injections. The game, with such even tools for both sides, no longer resembles a gambler [Terran] vs. a casino [Zerg], but, combined with the fast paced action, is almost directly relatable to lightning speed chess.
In the same likeness as lightning speed chess, losing material is insignificant; the only important thing one should remember is that a sacrifice is meant to lead to a greater advantage that normally would not be available had the sacrifice not happened. With this in mind, we find Terrans who lose every engagement, but aim to kill hatcheries instead winning, and those Terrans with fierce battle mechanics, akin to Polt and Innovation, demolishing Zerg's who would dare to set the game up on the teetering saw of battle.
The Zerg meta-style, since the beginning of SC2, has been to sit back and barely defend and defend until you have the perfect army against Terran or the perfect economy against Protoss and win. In HoTS, with the advent of all these new tools for Terran, Zerg's style has to change; perfect defense cannot work against someone with the same, but stronger tools you have. How did Terran win TvZ in WoL? Aggressive maneuvers that pulled the Zerg out of position for another attack. TvZ then was entirely based on Terran gambits and furthered by stronger and stronger gambits.
Now TvZ is an entirely different beast, and from here on out it is purely my opinion on the way TvZ should be done from the Zerg's side.
1) Mutalisks should be ousted from the matchup.
2) Infestors must be brought back into the matchup.
3) Vipers should be implemented as much as possible.
4) Drop defense should be done purely with static defense.
5) The Zerg should defend no more than 5 bases at a time with static defense, with 4 of them being mining bases and the fifth being the main base where the tech should be.
6) Drop defense should be rated in this priority:
-Base where the tech structures are held
-Newest Mining bases
-Oldest Mining bases
Let me explain each of my points besides p. 6.
1) Mutalisks should actually be gotten rid of. We can see with boosters, Mutalisks fail to catch up with medivacs; not only that, attacking a Terran's mining base is almost always a terrible decision with the lack of dps and ability to only kill workers efficiently. To make it obvious to anyone that doesn't get it, mutalisks suck in terms of killing buildings; not only that, killing buildings sucks for the Zerg to do anyways because of the multiple amounts of production facilities the Terran has to produce on the same scale as the Zerg. Also, they are now terrible vs. MMMM because they just can't kill medivacs anymore with This seriously means that Mutalisks have only one purpose in TvZ and that is to kill workers. The reason this can actually be considered a minor objective is that Terran production is just so low cost that Zerg has no reason to actually killl workers; in fact, it's actually better if the Terran can just build more workers because it takes away from his army supply, rather than helping him free up his supply. And what is he gonna zip up his supply with? Marines, which counter Mutalisks. It makes no sense for you to help your opponent kill you better.
2) Infestors may not be as strong as they once were, but the best part about them is their ability to counter maneuverability with Fungal Growth. This is extremely helpful when fending off MMMM because the Terran is now forced into mixing in marauders with his army. What's the best part about Marauders? They don't shoot up, and they suck vs. zerglings. They only thing they are good at in TvZ is tanking shots from blings. Also, another great thing about Terran's getting marauders is that they are spending a larger amount of gas than they originally were, so their tech or their widow mine production has to be slowed down. Either scenario is good for Zerg.
The best thing to think about is Infestors they are equally useful in small numbers as they are in large numbers for TvZ. 4-5 Infestors cause as much damage as 8-10 because all engagements only last for 15 seconds at most in TvZ. This means that the damage that is output is used in those 15 seconds cannot be one for one only, but has to be splash. The longer the engagement lasts, the better Zerg's chances are in it (once the widow mine shots are done, the only thing left is marines and marauders, and the more they split, the stronger and stronger zerglings become because the surface area for each ball has decreased and each ball is at a range where all the zerglings are not able to be targeted at once). Anyways, because of that, Infestors will help blings land more often as well as FF from widow mines.
3) Vipers actually have great syngery with Infestors; if you're going to follow point 2, you should naturally accept that Vipers will devastate the Terran's attack power while also making it even more likely of an FF shot from a widow mine.
4) This one I honestly believe; drop defense with an army sucks. The point of the army is to engage, not be stuck back at home defending. The idea of your army's position relates to what area of the map you are exerting pressure on; if you're army is in your base, you exert pressure on no area of the map that is being contested. Defence from drops should, whenever you can, be done with static defenses. Honestly, this is how it should be: Spine crawlers in your mineral line, spores near the edges.
5) You should never really have a reason to be running more than 5 active bases, where 1 being your tech stronghold and the rest being economic purpose only. The reason for this is that you shouldn't be able to deal with multiple drops from the Terran (regardless of whether you have mutalisks or not), so why spread yourself too thin? Your aim should be to not lose from Terran's drops as well as maintaining a strong enough army to battle Terran's army so that you can push into Terran's base. There is no point at all in making one of these jobs harder for yourself just so the other can be minimally helped (a la 7 base Zerg trying to harvest larvae just so his already maxed out Zerg army which is super weak can be revived again to kill Terran).
In a game where both sides have the same tools, and one of them has an edge in the strength of the tool, the other side has to make do taking away the advantage and pushing forth their own advantages.
Zerg no longer has the unbeatable late game advantage. Now, they're advantage is the ability to stop mobility along with their own mobility. It's time to abuse that.