I have no personal experience with a drop trap, YET, but I am sure I will some day. I have watched someone use it thought.
THE PROS: I have been told by people who have used them that this is the ‘go to’ trap for cats that have become ‘trap savvy’. They have been trapped once, or maybe even twice, before but have escaped. Or, they have watched other cats in the colony get trapped. This trap gives the trapper enough room to put a big plate of food on the ground to entice the cat.
THE CONS: Some cats are like Houdini. They can get out of anything. If this trap is not placed on flat ground, the slightest opening can give them a way out. The other problem is that your MUST transfer the cat in to another trap or crate to take them to the vet. Not easy with cats, for sure. They are bulky and cumbersome to handle and you MUST be there use a rope to pull the trap down, which means, you must stay there until the cat is safely under the trap. When you consider the process, you can see, it would be easy to have the cat escape.
Here is an image and this is an additional link to full instructions on using a drop trap: Drop Trap YouTube Video
A little secret on keeping them safer. I was, like most, concerned about them dropping down on a cat, if the cat moved quickly or had a body part hanging over the edge. A lady used water pipe insulation tubes that are already split along the length to easily be put on for cold weather. Put them on the edge of the bottom and that will protect the cat a little better.