What's the difference between the wargear you get in SP and the Last Stand?

Everything. They do not port over to each other. There are totally separate game modes.

Are they the same equipment though?

And the packs that you buy, which mode does it affect?

Not really, the campaign has much more interesting and varied wargear that drops at random pretty much, usually with unique stats, name, and descriptions like a plasma gun named "Tiger Fury" that does extra damage to Chaos.
In Last Stand, each hero unlocks a specific peice of gear at each level, like "Plasma Gun."
They are the same in the sense they are both Plasma Guns, but they have totally different stats and stuff.
The Packs are for the SP campaign.

How does this game compare to Dark Crusade? (in terms of richness, depth and complexity, where the first two DOWII titles had little)

Are these games worth getting? I know Relic did a great job with CoH, if the gameplay is as good as that I'll have to pick it up. I've always liked the Warhammer universe but I've never been able to get into it, seems like a pretty good place to start.

If you liked CoH, this might be more of a game for you. The old DoW was more of a squad-based StarCraft (Talk about irony...), DoW2 went more into the direction of CoH and took the hero units of WarCraft III with it while slaughtering along.