"If Canada abolished the monarchy or changed the succession rules it would have no impact on the UK. Conversely, if the UK were to change its succession rules and Canada maintained the status quo, we would be faced with the possibility of having to completely change our system to accomodate a resident monarchy - when our political system and constitution are not designed for an absentee monarch (hence the position of governor general which does not exist in the UK). TAB 

The ""British monarchy"" is ""first among equals"" in political terms as the abolition of the monarchy in Canada, Australia, New Zealand, etc would have no impact on the monarchy in Britain whereas the abolition of the monarchy in the UK would almost certainly lead to its extinction in the rest of the Commonwealth Realms.

The fact is that the system in the ""Commonwealth Realms"" (outside of the UK) was designed with the assumption that the monarch would be resident in London. Do you deny that?TAB

The fact is that the monarch is present most of the time in Britain. She has spent 2% of her reign in Canada and, I suspect, around that percentage or less in the other Commonwealth Realms.TAB

The fact is that this means there is quite a different relationship between the monarch and a) her British subjects and the British political system and b) her subjects and the political systems in the other Commonwealth realms.

The most obvious constitutional difference is that the duties and constitutional role played by the Governor General in the Commonwealth Realms is played by the Queen herself in Britain. i.e. The Queen, with increasingly rare exceptions, does not give royal assent to bills passed in Commonwealth legislatures or even give the Throne Speech (what in Britain is called the Queen's Speech because the Queen herself gives it). She does not name the Prime Ministers in Commonwealth Realms, does not resolve constitutional or parliamentary crises that may result in Commonwealth Realms and does not have weekly meetings with her Commonwealth PMs.TAB

Now monarchists like to believe that the Queen is fully informed and intimately involved in, let's say, Canadian affairs. The reality is that in the Commonwealth Realms the role of the monarchy has developed so that it is really more of an abstract and theoretical entity, much more so than in Britain.TAB

Let me give you a hard example. We now know that the Queen was not at all consulted on the dismissal of Gough Whitlam in Australia in 1975. This was done by Governor General Kerr in her name but she was not consulted or even informed until after it had happened.TAB

Let me give you another example. We now know thanks to the 30 year disclosure rule that the Prince Philip and the Prince of Wales quite regularly write letters and make phone calls to Cabinet ministers and senior bureaucrats in Britain complaining of this or that government policy (this is actually quite shocking considering all the propaganda we are fed about the monarchy being ""above politics""). We also know from biographies and autobiographies that UK Prime Ministers do give some consideration to what the Queen thinks about this or that thing or even this or that minister. It may not be a decisive consideration but its in the picture. That is simply not the case for Commonwealth Realm PMs. There is no evidence of royals writing Canadian or Austrlain ministers complaining about this or that policy or of Canadian or Australian PMs being particularly concerned about what the Queen might think, at least not to the extent as is the case in the UK. TAB

Now you might say but the Governor General acts on HMs behalf so there's really no difference. But there is, the Queen's role in the UK is unmediated, in the realms it is mediated by a GG and she is almost a complete absentee from the process.TAB

Therefore, it's quite clear that her role is much more important in the UK than elsewhere. 

Also, the fact that the systems in the Commonwealth Realms are designed with an absentee monarch in mind and have a GG in place Britain becoming a republic would have an impact on the realms where Commonwealth realms becoming republics has had no impact on the Queen's role in the UK. 

The fact is if Britain became a republic the Commonwealth Realms would have to figure out which one of them would become the new home for the Windsors, or if some sort of shared custody arrangement should be worked out where, say, she spends one month in each realm.TAB

The fact is they would also have to deal with the royal family's wishes, including the possibility that they would not want to move to Canada or Australia but would prefer to either remain in a British republic as ordinary citizens or live in exile in Europe (or even the US). That would raise the possibility of abdication and having to find a new mon