Combos needn't have anything to do with it. Beatdown, in my mind, is all about speed. It needs to inflict itself upon its enemy before that enemy has a chance to realize what's happening, much less set up its own ways of stopping the beatdown. The best example of this I can think of is a good Goblin deck, which is lightning-fast and will win in four or five turns if you can't figure out a way to stop it.
Having said that, I remember most of my MtG playing would have been beatdown oriented, with little or no focus on any particular combo.
The Control deck is just one that can stall the Beatdown long enough to set up its own, slower victory conditions. Think of a green or a white deck, with some cheap blockers and life regeneration, which needs to stall until it can build up the mana to unleash huge creatures to stomp all over the enemy.
When thinking about this in terms of Warhammer, it's less about speed and more about inflicting vs. controlling. The 40 Beatdown army isn't necessarily faster, but like the beatdown deck, it's very single-minded, and from the very beginning of the game it immediately tries to define the conflict in terms of its own playstyle. Therefore, a shooty Earth army will get into good cover, spread out, and generally make it hard to kill them. They will begin shooting the closest approaching enemies, and continue to do so all game. In this manner, they seek to ensure that no close combat occurs, and thereby define the terms of conflict as "shoot and outlast the enemy." On the other hand, the cc Fire army will deploy centrally and forward, and will surge forward as one, doing everything in its power to engage the enemy in melee, thereby defining the terms of conflict as "assault and deal as much damage as possible as quickly as possible."
Similarly, the 40k Control list isn't about lasting longer, it's about not letting the Beatdown army define the terms of conflict. The control army is usually highly mobile, letting it avoid CC with aggressive armies, and also letting it seek out and engage in CC with defensive armies. Control armies are not necessarily more well-rounded than Beatdown lists, since a single-minded Earth list will play control to a single-minded Fire list. However, the Water army DOES need to be well-rounded, because it wants to play control against ALL other lists, and so needs to be able to control multiple different types of enemy armies. By being versatile, the Water army can always seek to shift the terms of conflict away from whatever its opponent wants them to be. In this way, the Water list, which is moderately capable in all aspects of the game, will be able to overcome the beatdown list, which is excellent in one aspect of the game but inadequate in all others.