Not much of an advantage either way, except that a domain endingin .uk makes it clear that the company is registered in theUK.There might also be differences in the registration cost, andprocess, since different top-level domains are often handled bydifferent organizations.But in general, you would probably choose whichever domain youthink is more memorable to potential visitors of the website. - Youcan also choose to set up more than one domain; many companies dothat, and quite often, one of the domains will redirect to theother one.