[RightDeve]

Yes, there's actually a difference. Might better lower your in-game text speed in the preferences screen and you'll see this message ***Structure Collapses*** on the bottom of the screen if you have a building smashed completely by heavy arty or bulldozed by heavy or engineer tanks.

Try playing scenario number 17 "South of Beirut", there's a couple of zionist bulldozers you can use to "collapse" some buildings.

I don't know exactly which one is better for cover, "collapsed" or "destroyed/damaged" buildings but I have a feeling that collapsed ones are less capable of offering covers due to their being completely smashed off already. There's still a good deal of movement cost required to traverse either type be it vehicle or infantry. But there's one difference: your tanks or any vehicles will not be immobilized if you go through collapsed buildings, unlike those damaged buildings.

"Damaged" buildings I think are those which have received some damage to their structure but still standing and hence the rubble coupled with the still standing structure create a maze perfect for cover. "Collapsed" ones are those completely smashed off to the ground and may incur casualties to any units experiencing the collapse inside.

AFAIK