If you're an entrepreneur and want to kill a deal with a big company in the cradle, then follow the advice of 'Uncle Saul' in a post (otherwise full of good advice) on negotiating such contracts. See Kiss of Death – Contract Provisions Entrepreneurs Should Avoid at All Costs (hat tip: Hacker News). The author explains why he thinks an entrepreneur should "never agree to ... allow the other side to draft the agreement ...." That's unrealistic, if you ask me.
For reasons good and bad, big companies usually want to use their contract forms, not yours. Certainly it's important to offer to draft the contract. And if the big company reeaally wants to do a deal with you, then you might get away with insisting on controlling the typewriter.
But bad things can happen, though, if you simply fold your arms and refuse to negotiate the other side's contract paper. Even if the big company's negotiators grudgingly agree to work from your draft contract, they'll start the negotiation thinking your company is less than cooperative (which isn't good for the business relationship). Then later, when you ask for a substantive concession that's important to you, they may be less willing to go along. In any case, their agreement to use your contract form, in their minds, will be a concession on their part, meaning that you now owe them a concession.
For a vendor lawyer, there's another danger in insisting on using your own contract form: Your client's sales people will blame their lack of progress on you. Sales folks are always having to explain to their bosses why they haven't yet closed Deal X. Your insistence on using your contract form gives them a ready-made excuse: They can tell their boss that you're holding up the deal over (what they think is) some sort of petty legal bulls__t. Even if that's not the whole story, it's still not the kind of tale you want circulating among your client's business people.