Neither, since both countries effectively continued with monarchies with another name. We ourselves tried that before with a Lord Protector, and while it worked in the short-term, it ultimately centralized power in a marginally more numerous economic elite.
Despite the disturbing lunacy of the royal baby crowds the other day, the vast majority of UK citizens are largely apathetic about the monarchy, and the Scottish in particular have been broadly republican for years. The biggest obstacle in the way of republicanism is the fact that republicans insist on proposing presidencies as an alternative, and Britons, for all their flaws, rightly despise the corruption and personality cults of presidencies in either their weak or strong modes. The easiest path to republicanism in the UK is to simply point out that the monarchy here has no function and therefore requires no replacement by anything, particularly anything resembling the US, French and Russian presidencies.