Just came across these Fire Emblem banner ads on The Escapist and thought they were very clever. http://www.fire-emblem.com/shadowdragon/secondstep/index.html They dial right in to what the game's about: tactical choices. If that's your kind of thing, you'll know Fire Emblem is for you. It was already on my GameFly queue, but if it wasn't it would be.
On the other hand, it also illustrates the problem with highly tactical games. It's fairly easy to crunch the numbers and figure out which choice is the right one. You always counter scissors with rock; there's no meaningful or interesting choice there. A game has to give you trade-offs, guns vs. butter, (in other words, fewer guns now for more guns later) to make you start to agonize over your decisions. And when a game does that, your mind enters into this new state - you're not sure about the right decision. You reason as much as possible and then trust your gut. Playing the game stops feeling like a science and starts feeling like an art.
A recent example for me on the strategy-above-tactics front is my friend Lars Doucet's Super Energy Apocalypse - where each kind of power plant you can create has its own set of negatives: coal & gas create smog which power monsters; nuclear creates nuclear waste which the monsters like to run off and use to become super; wind and sun aren't always there for you; and geothermal, which has no negatives, only has a few spots on the map where it can be used. And while you can probably get through the game (on medium difficulty, anyhow) with any of them, maximizing your score requires thought and practice. It's also pretty funny.
The downside of games that place more emphasis on strategy? Tactical decisions usually become irrelevant. It doesn't matter if you execute a brilliant flank or counter when you're dominating strategically and your forces vastly outnumber your opponent. With some RTS's, when you dominate economically, it no longer matters which unit you build - all that tactical breadth the designers incorporated rendered meaningless. It makes me sometimes wish there was no economy, so I could meet on the battlefield with equal forces and see who makes the best tactical choices. (But then when I come across an RTS that takes the economy out, like Myth, and have gotten what I wished for, and it's more of a puzzle game than a strategy game, I discover that I'm quickly bored.)
Bottom line: a game designer can't win, but erring on the side of emphasizing strategy seems to me is usually the way to go.