I file tax returns in both countries. Because there is a tax treaty between the US and Canada, I am not subject to double taxation so I get a credit for the tax I pay to Canada. Since Canada has a higher tax rate than the US by and large, I don't end up owing the US much if any tax.
There are exceptions though that are significant. In Canada we have a tax free savings account which is something similar to a Roth IRA. This is not recognized in the US. Therefore any interest I make on such an account would be taxable in the US, even though its not in Canada. As a result, I am unable to open such an account in Canada because it serves me no purpose. Similarly we have a Registered Education Savings Plan (there is something similar in the US but I don't know the name). We had to put my kids plan in my husband's name only because if my name were on it, it would be taxed in the US. There are other things, including house sales that are taxed differently in different countries. The kicker for me is that the US has a death tax. I am primarily a SAHM so when I die the bulk of my estate will be from my Canadian husband's earnings. Before that estate passes to our Canadian children it would be subject to US taxation. Keep in mind that none of this money has any link to the US.
The person who benefits the most from this is my cross-border accountant because its impossible for me (or any ex-pat) to navigate this system. Even though the tax I end up paying to the US is negligible, my accounting fees are significant.
In any case, all I'm saying is that the decision to renounce or not renounce ends up being a practical one rather than a patriotic one. I know many Americans who are very sad to give up their US citizenship, but in order to protect the finances of their Canadian families they have no choice but to do so.
I haven't renounced my citizenship yet
but its definitely something that is always on my mind.