I found the information in the website very interesting. Britain and Belgium have constitutional monarchs. I think that the main difference is that there is a written constitution in the case of Belgium and an unwritten one in the case of the United Kingdom. In some respects, an unwritten constitution, allows for greater parliamentary control; whereas, in Belgium both institutions have defined roles.
Recently, I read that the Belgium government was to pass laws in the very short interregnum between monarchs to allow for the new monarch to pay income tax. If, I understand matters correctly, this would not occur in the UK because there is no break in the monarchy because of the principle - 'The King is dead.Long live the King' concept ensures that there is no time when there is not a monarch.
Does this mean that the new monarch of Belgium has less powers than his father? I doubt it. Constitutional monarchs have to sign bills/laws passed by their equivalent of parliament or abdicate -if push comes to shove, as the saying goes.