And since each has its merits, you decided to choose based on compensation
I can think of a handful of companies off the top of my head that would immediately rescind the offer if you made this proclamation. I'd be careful about doing so.
A rescinded offer is, at least from what I've seen, unlikely. The person is more likely to be hired but with an already negative reputation, not be successful in the company, and be laid off or fired early on. How it plays out: after 6 months, the person is let go with 3 months' severance not to disparage the company. That's actually a small price to pay for silence: 9 months' pay for 6 months of work and a gag rule. If the offer is rescinded outright, there's no chance to draw up a severance contract and that person will damage the company's reputation and make recruiting harder. The added recruiting difficulty might not be much (maybe 5-10% in the candidate's school/network and 0.25-0.50% globally due to negative internet posts) but firms don't want to take that risk, because recruiting is seriously expensive and hard.
This is why companies don't rescind offers unless people do something really bad. It's much less risky to have the person work for a few months, fire the person if he or she doesn't disprove the negative opinion (which is hard to do, because once a negative opinion is formed of a person, it's almost impossible for that person to change it) created by the bad behavior, and get a non-disparagement clause in severance.
What this means is: just because you're hired doesn't mean they actually like you. The post-offer stage and first 180 days of any job should be considered an extended interview. In that light, respectful negotiation is actually a good thing but being a jerk is not. Saying "I'm going to choose based on compensation" makes a really shitty impression. It's best to say, "I think I'm actually worth $<X> and here's why." Also: don't mention other firms or their pay packages, ever. One of the easiest and most common ways to make a bad impression in job searching is to disclose sensitive information (and competitors' salaries qualify).
I can think of a handful of companies off the top of my head that would immediately rescind the offer if you made this proclamation. I'd be careful about doing so.