What would I get? I'm vegetarian

If you're willing to stray from Campbell's, you could try Amy's No-Chicken Noodle.

Bevi is right.

I suggest tabling any attempt at making corn stock from scratch for now. It's great when you have leftover cobs, but it's silly to consider in the dead of winter.

Note that the Saveur recipe was posted in the month of August.

Since you are asking which other can of Campbell's soup to replace their chicken noodle soup, I am guessing that you have no desire to make your own vegetable stock from scratch.

Just buy the Campbell's Vegetarian Vegetable can (if you are stickler following brands) or replace with some other brand's vegetarian vegetable soup.

Lapadia makes a stock out of corn husks and cobs. http://food52.com/recipes/14787-spiced-corn-soup-w-corn-husk-stock

I think it would be fantastic as the base for whatever kind of chowder you wind up making. Maybe too labor intensive or not seasonal for the corn, but something to think about in the future.

What you'll get with all of the canned soup and corn is a lot of salt, and probably a fair amount of sugar as well. I vote for the Saveur recipe as well!

It's a little bit more of a project than opening a can of soup, but just in case you want to try it sometime you can also make corn stock and use that for extra-corny corn chowder. Here's a recipe from Saveur: http://www.saveur.com/article/Recipes/Corn-Stock

Agree veg or mushroom or bean broth as sub for chicken noodle soup. Optional add some thin noodles.

a simple vegetable stock would work just fine! (and you could add noodles later, if you wanted.)