For greenfly, couldn't you get a ladybird to eat them instead of having to throw them away? I agree with the hassle of windowsill insects that just mysteriously appear, though. My aloe vera kept getting this white webby cocoons of something, and my tarragon developed tiny brown scales.
Back on topic, the fresh versus dry (versus frozen) depends on the herb. And maybe even depends on the specific dish that you're putting herbs in to.
I'd rather have fresh basil (although, just like SatNavSaysStraightOn I have had so much trouble keeping them alive (when every other guide says that it's a hardy plant that is easy to grow??)
On the other hand, I prefer to dry the Italian oregano that I grow myself. It gets rid of the sting that the leaves have when they're fresh.