I think that the general consensus is to have a trash can near both if possible. I put a double trash next to my prep sink, but at the clean-up sink, I have a pullout under the sink which holds a smaller can. I did not want to give up another cabinet for separate trash there.

Also, see if you can have two disposals.

Trash is not generated during prep, unless you are talking about the cardboard box that the frozen dinner came in. Scraps either goes in freezer bags for stock first, or a very small amount goes directly in the compost. Washing is done before prep, and the majority of prep can be done while cooking unless you are having a big party or producing a TV show. Why would you want to stretch cooking into an all day project by separating tasks instead of multitasking?

I used to have a prep sink and I did have a small trash can underneath the sink there. I think it would have been better to have had a bigger one, but space didn't allow. I did have a disposal in both sinks and I highly recommend that.

Have a trash next to clean up and prep areas. After a very scientific study, the prep area trash fills up at least 3x more quickly.

In my previous home, where the prep sink and the main sink were far apart, I had a pull-out cabinet 2-trash can (1 for recycle) system beside my main sink (clean-up after meals), and a can under the sink (inside cabinet) for prep.

In my small kitchen in my current home, the sinks are close enough to use the pull-out beside the main....which I open when at the prep so I can toss things towards it.

All that said, I often use a big stainless bowl to collect waste while prepping, then dispose of it after I'm finished.

I have a trash/recycling next to my prep sink and a small trash can under my cleanup sink. Like Sophie said, most trash is generated by the prep space, but there are also things that need to be scraped occasionally which is why I'm having a separate trash under the cleanup sink.

And as someone else suggested, I'm having a disposal at each sink.