It's nothing compared to here!

Okay, LA has a huge Koreatown while Chicago has a small one.
I want to express that LA's Koreatown is much much bigger than Chicago's Koreatown.
Then which one should I say to emphasize the difference of their sizes?
a) "LA's Koreatown is nothing compared to Chicago's Koreatown."
b) "Chicago's Koreatown is nothing compared to LA's Koreatown."

Let me ask you one more question:
Which verb usually goes/fits with the word "grocery shopping"?

a) Would you like to "do" grocery shopping?
b) I have to "go" to grocery.
Is it "do grocery" or "go grocery"?

"Chicago's Koreatown is nothing compared to LA's Koreatown" means that LA's is bigger. It dwarfs Chicago's.

I've only ever heard "I'm going grocery shopping" or "I've gotta go get groceries" etc. Although I wouldn't doubt if those folks in New Orleans say something like "do groceries."

If you like the verb "do", you could always say:

a) Would you like to do some grocery shopping?

-or-

a) Would you like to go do some grocery shopping?



and (b) should be:

b) I have to go to the grocery.

Logically, it should just be "I need to shop for groceries", but it's a common phenomenon in English that a verb gets put into a noun phrase and stays there. Hence "problem solving" instead of "solving problems", etc.