I haven't used a tray before, but the stamp is super easy to use. I don't think it's that difficult to fill them equally and I think the stamp would be more flexible than the tray for when you have "oopsies" you can just repress the individual stamp, instead of messing with a whole tray... but again, I've only used a stamp.

I haven't used either, but if you have a kitchen aid stand mixer their ravioli stuffing attachment works great if you have nice long sheets of pasta.
Ravioli Attachment Page - There is a video you can see it being used there.

We have a tray and my husband LOVES it. Just roll out a couple of sheets of pasta and then you have 10 raviolis made in no time!

I have a tray and I love it. I've never used a stamp, though, but I like the speed of the tray. I've never had trouble with "oopsies", and if you did have one that was ruined it wouldn't ruin the whole tray, you could just reincorporate the dough into what you had left and try again with the next batch.

I have a stamp. It's okay for making a small batch, but rather slow and tedious if making a large batch. And, really, it's not needed at all: a sharp knife will do the trick just fine.

The only way I've ever made ravioli is using a pierogi/dumpling/mini-pie press. However that was because I was using pre-made dough rounds.
If I had a lovely long sheet of dough I wouldn't use anything but a crinkle dough cutter (the wheely thing). Just place your filling, put the top dough piece on, mold lightly with your hands and then trim with the wheel.

Then again I hate uni-taskers in the kitchen, so take my words with big grains of salt.

I have a press, and while I love it, I learned making a giant batch of ravioli for Easter dinner that it is insanely tedious. It's fine for a couple, but this year I'm investing in a tray.

Has anybody used the Imperia ravioli maker? I have had no luck with this, the pasta sheets tend to tear in the rolling mechanism. I am definitely investigating other options to speed up ravioli making!

+1 for the crinkle dough cutter (the wheely thing)

I have a tray, I like it, it makes very nice sized ravioli with crinkle edges (just like the photo of the one above does).
Having made free hand ones with biscuit cutters and a fork or pie crust crimp, I think the tray is superior because you don't have to pat the dough around each pile of filling to ensure the least air. You lay the dough onto the tray, put the cupped tray onto it to stretch and make the pockets, fill the depressions level, and lay another piece of pasta on top, and run a rolling pin over it. 12 tight, identical ravioli. (mine makes 12) Now if you want larger or smaller ravioli, then something else.
I've looked at the Kitchenaid/Atlas attachments and the comments are always that the filling gets underneath everything as the two sheets are pressed together- but I don't know this first hand.

@ Stan, I didn't know the process for a tray, so thank you. Does that mean you'll have 2 different thicknesses of pasta though? Does that affect cooking?

Put my vote down for the wheely cutter as well. Works for pie lattice and cookies too plus slim and easy to store.

It's $5 at WS here: Fluted Pastry Wheel, but I've seen it even cheaper sometimes.

I use this roller and it works great. It saves on storage space too!

@food lover not fighter -- Oh, I always see those when I'm thrifting but never really knew what they were for! Interesting and good to know!

This is why The Kitchn readers are awesome -- thanks for all the responses! So far I think the tray is winning in my book, but I'll look more into the pastry wheels and the roller since I didn't consider them much before. Keep those opinions coming. :)

@ food lover not fighter: I would totally use that for soup dumplings, it's genious. Not sure about ravioli though, would you use the stamp to make the seal?

I have the Imperia attachment and I find that my roller or stamp work much better.

Having only used a roller, I would have to say anything is better than it. With a roller, you have to lay a sheet down, fold it in half lengthwise and make a little indentation or mental mark for the midway point, try to evenly space the filling on one half, fold over, try to get all the air out (not as easy as it sounds), then cut and trim. It's extremely tedious and inconsistent.

I enjoy making ravioli with only a parking knife. They don't have crinkly edges, but I can make them any size I want, which is quite satisfying.

Another one for the pastry wheel! The trick is to make the one with crinkles slightly larger and then the other one without crinkles smaller to keep the crinkle shape.

Ohhh, good point, @amidalilama. Thanks for the tip!