If both hot and cold pressure drop off when you push the faucet to full, its one of two problems.
The first is something either broken or blocking the opening to the spout inside the cartridge.
If I hadda make a guess, I'd suggest the cartridge replacement. It should eliminate all possibilities. Before you replace the cartridge though, you might want to check the sprayer head to see if there is anything on the inside. You can do this by pulling the head out of its holder and unscrewing it from the hose. Turn the water on and see if the water pressure is fine without the head on. If it flows perfectly there is someting in the head.