I'll make an additional comment. From your description, it does not appear that either company has made you an offer yet. At this stage in the game, you don't really have much leverage. Job offers in hand are leverage. Your strategy should be to continue forward in parellel with as many companies as you can. Snagging a job offer from one is the best way to improve you chances with all the others. Having two offers (or more) gives you much, much better chance of optimizing your situation -- when companies are aware that their offer is not the only one on the table, they have more incentive to work to sweeten the package for you. All this to say: the idea of 'buying time' is totally the wrong way to be thinking about this; it pushes things in the wrong direction timeline-wise, since you want to moving things forward on all fronts to secure those job offers. There's no time to buy until you have at least one job offer.
Maybe they didn’t have the budget to hire you, and the other guy was cheaper. Now the other guy has flaked and the CEO has taken a 10% pay cut to hire you. I have been the CEO taking the cut to stretch for a candidate before.
You don’t know what’s going on behind the scenes, so be classy and polite, they may be stretching for you
No need to pressure them in any other way until they tell you what they see as the next step. Do not assume you have any leverage with them. They are probably also still looking. This is a chance to show them that you are a class act.
Don't look at this in any other way except as an opportunity. Yes, you can bring up the fact that another company is interested, but not at this time. Set the hook with class and an obvious interest in their company.