I am inclined to take a slightly different view from
@Zimba.
Firstly, as
@CULLINAN's
link above states, while the rules for ILR are aligned across the UK and the Crown Dependencies, the ILR granted in a Crown Dependency is not identical to one issued in the UK.
Schedule 4 of the Immigration Act 1971 explicitly integrates UK immigration law with that of each Crown Dependency. It says that applying for a visa for one of the Crown Dependencies is as if you are applying for a UK visa. But this does not mean that you are being granted a visa for entry or residence in the UK, only that it is being granted by the United Kingdom through the UK’s administrative and legislative processes.
...
if you have a visa from one of the Crown Dependencies – you are permitted to subsequently visit the United Kingdom. If you wish to live and work in the UK, however, you would need to apply for a separate UK visa.
Indeed, keep in mind that the same also applies to each Crown Dependency. An ILR issued by Jersey may not confer the right to reside in Guernsey or Alderney or Sark, let alone the Isle of Man.
Secondly, as Zimba said above, there is only one British citizenship. However, a naturalisation certificate issued in Jersey would likely be treated differently for some purposes to one issued in the UK.
For a start, the British passport issued to somebody whose only claim to British citizenship is via a Crown dependency is
visibly different. And till recently, such a person would have been an EU citizen, but without freedom of movement rights in the rest of the EU. So there are material differences between a naturalisation certificate issued by Jersey and one issued by the Home Office in London, even though they confer the same British citizenship.
At another level, where you naturalise could have consequences if the UK were to break up at some time in the future. Before 1983, the Citizenship of the UK and Colonies was the same across the British Empire. But, as countries became independent, the people who naturalised in the then-colony acquired the citizenship of that (now-independent) country, not that of the UK.
Where one naturalises can have implications years and generations into the future. I remember advising on these forums on a a case where the person's grandfather had naturalised in the 1920s and the nature of that naturalisation had implications on whether the grandson could acquire British citizenship now.
I hope that this gives you a fuller and broader picture of the situation, from which you can make your own conclusions.