Is there a benefit to building the larger versions of stores?

Question

There are three versions of each store to build in settlements, small med and large. Do they sell different goods? Do they generate more income?

Answer 1

On the first question, yes, the larger stores will carry better, rarer items. Uncommon crafting materials like Nuclear Material are more likely to appear in the better stores than the first store, for example. In fact I'm not even sure if the smaller stores CAN get all of the items, even at reduced chances.

Source, the Wiki.

There are a total 6 types of stores in the settlement build mode each selling different items. There are 3 levels of each type, requiring an increasing amount of caps, materials and perk levels to build, but also yield more caps and have a wider selection of goods in stock. ... These stores not only provide extra income and settlement happiness, but the Sole Survivor can also buy and sell items here. Higher levels of stores provide a wider selection of higher level and more rare items.

Seems like you get more caps for the better ones as well.

Answer 2

There is an additional benefit of building the larger stores.

If you build a level 3 store, and assign the right legendary settler to it, they will offer specific legendary items that you can't find anywhere else.

For instance, you can buy the Apocalypse Left Greave from one such merchant. (minor spoilers in the link).