RedBar, I agree with goodroi that, with regard to Google, .asia should rank as well as .com. The gTLDs are treated equally by Google. That said, as both goodroi and Dimitri mention, there are potential downsides to the .asia TLD from the point-of-view of users, journalists, etc.
To mitigate (most of) these, IMO you absolutely must retain the .com and keep it 301ed to the .asia.
My quandry was whether G would actually rank it as an "equal" to .com?
Yes, to add to the reassurances already give... all
other things being equal... Google would treat both of them equally in search.
The biggest risk you run, I'm thinking (and I've seen this happen more than once) is that, at some point, someone in your company is going to get the bright idea that they can save $20/yr or whatever it becomes by dropping the .com... and that it will get picked up by a domain squatter, who eventually might sell it back to the company for many thousands of dollars.
By starting out with the .asia gTLD, I should mention, you turn that domain variant into an albatross that you will need to carry around for a long while, whether the human recognition factor works out favorably for you or not.