Hello Liz,
I think the second is correct, cause the example is talking about actions not nouns so we use adjectives (e.g. loud) for nouns and adverbs (e.g. loudly) for verbs.
You can say :
Our singing was as loud as theirs.
We sang as loudly as we could.
Your ear was exactly right in this case. Your first sentence is just fine, and I’d say sentence 1 would also be the more commonly used of the two.
The word “loud” is used both as an adjective and as an adverb.
Used as an adverb, the word “loud” simply means “in a loud manner”.