Which is the better time of year to visit Italy (August or February) in terms of weather, crowds and cost?

You need to specify a region. Italy includes the Alps up north which, are popular and expensive (and cold/snowy, teens and 20's) in February, while areas like Tuscany are in low season at that time with coolish dreary weather and low rates.
Down in Sicilia (500 miles south) daytime highs are 60 in February and the tourist seasons are reversed.

You might have better luck posting this on hte Europe board!

August is when the majority of Italian businesses shut down for a month, and all the Italians head to the beaches for the month. I've never been there then, but I imagine all the cities are ghost towns. I'm not sure if that's good or bad.

I'd actually try to hold out for as close to September if not September myself. August most things close down as it is the holiday month for europeans. February could be fabulous on the coast or even Venice.