This depends a lot on how your RFP approached the project. If you gave opportunity, latitude or even a specific request for creative to be pitched, you will need to sharpen your pencil for this one. But, for the sake of efficiency, let's start by assuming that all creative is equal, and you are only comparing bids on the basis of cost.
Let's say you have 5 options. First go through, and mark each proposal with a number. Henceforth, refer to them by number instead of name to expedite notes and reference. This also helps to safeguard against a witty production company name winning favor on style over merit by sheer repetition.
FIRST: THE BOTTOM LINE (total cost of each bid). This is a poor factor to compare, as all bids offer different things, but since your going to do it anyway, we might as well account for it.
SECOND: THE PRODUCTION. What are you being billed for? "Is there money in this bid for Art department to build that custom set-piece? Oooo--this bid doesn't even have money in Art Department...red flag." You can learn a lot about how thoughtful, creative and informed a production company is by how they bid a project. You also can neutralize a lot of the difference between various bottom lines by understanding who really bid the project right.
THIRD: PRODUCTION AND INSURANCE FEES. Typically, insurance is charged at a rate of 3-5% of the production budget. Some clients carry their own production insurance, which would benefit you to use and lose this cost. Production fees range from 0-35% depending on the project needs, timeline, overall budget and other lessor factors. This percentage can be negotiated. However, remember that the production fee is the clear profit for the production company. If this amount is shaved too thin, there may be little incentive for the production company to prioritize your project. That said, if the creative is something the production company seems very excited about, they may be more willing to shave their fees to get the opportunity to shoot this project. It is a bit of "cat and mouse", but needs to be done.
FOURTH: TALENT. Is their 5 extras on this bid, and 25 on another? Which is more appropriate? Is their enough in this bid for a really good hero talent? Are all roles accounted for properly? Have agency fees been factored in? You can always opt to pay talent direct to guarantee efficiency in these areas. This has certain costs and benefits which we will not go deep into here.
FIFTH: POST PRODUCTION. Is post-production included in the bid? If not, does the creative director, director or production company have an editor or post house they like or work with for this type of project? It is important to get a firm handle on post costs prior to committing to a production company's bid.