Big sink on left small on right. At least that is the way
I like it.

Usually the small sink has the garbage disposal, and most want it handy for the dishwasher. So, it depends on your overall flow, and where the other cleanup things will be, including the trash. If you do not plan to get or use a dishwasher, then order the sink to fit your preferred washing method.

For using a dishwasher, I prefer the big sink on the left. GD is on the right and the large left sink holds pots/pans while I rinse smaller stuff to go in the DW.

DIL has the reverse and I find the small sink on the left useless when cleaning the kitchen.

I actually put my small on the left which is next to the prep area. I wanted to be able to scrape directly into the sink while I was cooking.
DW is on the other side though, and part of me wanted the garbage disposal on THAT side for clean up, but unless I had two garbage disposals installed I couldn't do both (lol) so I ended up picking the prep side.

I don't know about "should", but I'm right handed and I have the larger sink on the left with the garbage disposal. I tend to soak things in the large side and then dump it with the disposal running. Also, the dishwasher is to the left of my sink.

When I hand wash dishes I make a tub of soapy water on the right in the smaller sink, rinse on the left and then place in a countertop dish rack. (right to left)

Btw my GC said he usually puts the disposal on the smaller sink, but it's my house. :) I really like my set-up and wouldn't change it. Choose what you will be comfortable for you. Good luck!

We'll have the same setup as Jmfromil, except the DW will be on the right. Both DH and I are right-handed. The choices for the large/small bowl configuration and the locations of the GD and DW were my DH's since he does 80% of the cleanup. The kids are starting to as well, but DH still does the most.

I've looked at dozens of these sinks recently, and I don't remember one where the big sink was on the right.

Handedness matters, but not as much as relationship to the DW, IMO.

Seems to me the small one should be closer to the DW, and that the DW should be on the right for right handed people.

But: the DW should be on the same side of the kitchen as the dish storage, and the dish storage should be on the same side as the dining area-- makes for fewer steps.

So the small sink should be on the same side as your dining room.

It's official: I've overthought this...