I am no siding expert, but from looking at the two different estimates here's my take.

Are they using the same materials - I can't imagine that one contractor would charge you 4K and another charge you 13.2K for the same product.

It seems that #2 is giving you more things than #1 - I don't know what you would need in your situation (part would depend on how things look under the current siding they are removing).

I would also ask to see samples and get the names of the shingle they are quoting (there could be a big difference between the products).

We are residing our house as part of a remodel. They've wrapped the house in a Tyvek product. We had to insulate (turns out the original part of the house didn't have any insulation in the walls). We had them blow the insulation in from the outside in between the studs (we have noticed a difference and the siding isn't up yet).

I would ask neighbors/friends who have had their siding replaced and who they used if they are happy with it. I would also get additional estimates (and ask the first 2 contractors) to break down the estimate the same way (by material and labor) so you can compare apples to apples.

I would go to each and ask for an apples to apples compariso-- tell them how you want the bid to break down. And, yes, really check references.

Since you said you are taking it down to the studs the first guy has a bunch missing. What is he going to fasten the new shingels to. He didn't quote for and under layment material. The second guy did.
Cost of Tyvek air filtration and moisture barrier 1.3K
Cost of Celotex insulation and fiber board 4.5K
#2 is also priming the shingles.

You need to clarify exactly what each is doing and the materials being used.