The United Kingdom has mostly devolved issues that affect Northern Ireland to the Northern Irish government in Stormont. Northern Irish voters decide who sits in Stormont, giving Northern Irish residents the autonomy to determine how they are governed. While disagreements have led to its dissolution, it may well return soon and when it does, Northern Irish voters will have a greater voice and more autonomy than they would have in a United Ireland.
Even if Ireland does introduce provincial governments, the value of a Northern Irish vote would likely decline slightly as the other three counties of Ulster - Cavan, Monaghan and Donegal - are added to the Assembly. The United Kingdom is also set to become more democratic and allow voters a greater voice as it leaves the European Union. Meanwhile, the Republic of Ireland will remain under the eye of Brussels, which passes laws with virtually no input from the Irish voter.
In addition, the United Kingdom represents many diverse viewpoints and backgrounds: there is not a single, consistent "British" vote that is stifling Northern Ireland. Even within England, differences between voters are strong. Ireland, on the other hand, is so dominated by the size and economic power of Dublin that voters from the capital could easily form a single bloc to quash Northern Irish objectives.