I have Ikea cabinets, so YMMV. Our trash/recycling pull out is 18" wide and holds two tall Ikea bins perfectly. We have your first option with the top section as a drawer and then the lower section that just looks like two drawers. The drawer is handy for us--it's where I keep random, non cooking things like pens, tape, rubber bands, post its, scissors, post its, mini tool kit.

Entire height, the tall can is in the front with a shallow "scoop" at the rear which holds a 75 count roll of bags. LOVE the "scoop".

Full height so you can just scrape trash from the countertop into the open cabinet. A drawer front will just be in the way of tomatoes juices and veggie peels.

I wouldn't do a counter height pull out drawer if every other cabinet in your kitchen were not like that. I would match the lines of the rest of the kitchen. And then I wouldn't waste space by having a fake front. I have a drawer over my trash cans. It's an 18" cabinet and plenty of room for two trash cans.

I have the drawer over the full length cabinet. I like the drawer for trash bags, baggies, tinfoil and such. As for whether you face it with a cabinet or drawer face, I looked at it as it is a cabinet and not drawers, so cabinet front.