Suppose it seems to you that you ought to phi, but you also think that your judgment in this case could well be biased or otherwise impaired. You believe that other people in similar circumstances to yours have turned out to be mistaken. Moreover, others you consider to be moral experts -- reliably more insightful than yourself -- are unanimous in insisting that you should not phi. What should you do?
Objectivists must allow that appearances can be misleading, and so higher-order evidence can undermine our first-order beliefs. In the above scenario, it looks like your all-things-considered judgment should be that the totality of reasons that exist weigh against phi-ing, even though you do not currently have access to all those reasons yourself. The reasons in your possession count in favour of phi-ing, but as a realist you acknowledge that there may be other reasons beyond your grasp, and the views of experts can give you some indication of what the totality of reasons really favours.
What of the 'rooted' conservative/subjectivist? Here it is less clear. There may still be some room for overriding your personal judgments, e.g. if they rest on some merely empirical or logical error, and so do not really reflect your core values. But if we accept the Vellemanian position that what fundamentally matters is making sense to oneself, then there seems something deeply problematic about acting on mere "meta-reasons", i.e. the abstract promise of reasons out there that you have not fully grasped. You can't really make sense of your action, because even though there is abstract evidence that you did what is for the best, you do not yourself possess the grounds for this judgment; you don't, in other words, understand why it is for the best. So it may seem that you acted for reasons that are not, in some vital sense, your own.
This practical difference marks a vivid distinction between the two metaethical views. Whether we act for the sake of making internal sense to ourselves, or to make the external world better, will influence our receptivity to meta-reasons, and hence what decisions we make.
I take this to count in favour of objectivism, since it seems clear that we should be receptive to meta-reasons. As Dan Moller writes in 'Meta-reasoning and Practical Deliberation' [pdf] (p.26):
Failing to act on second-level reasoning means, by definition, acting on the basis of flawed deliberations when there is evidence of how improving those deliberations would affect the outcome. To return to the general [who is biased towards cowardice by the recent deaths of his friends], he presumably cares about discharging his duties as a soldier with integrity, so why shouldn’t he pursue every available opportunity to improve his decision-making? It is true that in that pursuit he may cut himself off from ultimate comprehension of the reasoning that leads to the conclusion to send in the troops, but accepting that limitation would in this circumstance express precisely a commitment to his deepest values and identity as a soldier, not any sort of compromise or abdication.
Isn't the alternative a bit solipsistic?