I have mixed feelings on the matter. Firstly, I can't think of any alternative political Heads of State (Presidents) in the whole world who command my respect. Can you think of any? If New Zealand became a republic their current prime minister is about the only one that does have something about her and she doesn't really operate on a world stage. I can't think of any UK politician (from any of the separate countries or any of the parties) that I would want to be President (Head of State), with increased powers. Secondly, our monarchy is largely a non-political and ceremonial position with no powers but with the capacity to influence and project the country on a world stage if they were capable and respected. The Queen has largely achieved that, but her successor, Charles, has almost certainly not. Skipping a generation to William may give the Royal family a better chance in terms of leadership, respect and modernisation.
Thirdly, I have always believed that the 'official' Royal family has always been too large, with too many hangers on. That is one thing I would have criticised the Queen for, including allowing the likes of Andrew and his family to exploit their status. Of course, in the case of Andrew, it has also stopped him being brought to account for his dubious activities. I would confine it to the direct line of succession and their spouse / children. The others should make their own way in the world. Give the Monarch an official residence in each country of the UK and a country retreat and return all the other properties and income to the state for alternative use.
Taking into account all 3 points above, on balance I think that our monarchy is better than an unremarkable presidential system that doesn't seem to attract capable and respected political incumbents in the world today