I'm not a fan of the distinction, as it is usually used by CaW fans to insult CaS players. CaW is for smart, strategic play, while CaS is for dummies who charge at at every monster.

Having played war games that cover both strategy/operational and tactical scales, I find that using both is boring - if you do well at strategy, the tactical battle is too easy.

I prefer CaS, as you usually have interesting tactical battles, while CaW is mostly about having the right spell for the job, or fast-talking the DM into letting you win without a dice roll (eg. setting the goblin caves on fire so they all immedately die from smoke as the adventure doesn't specifically mention ventilation).