The first (practical) issue is when grant proposals are due. CIHR proposals are due Sept. 15, and NIH proposals Oct. 5. (Both actually have to be in the hands of the UBC research administration a few days before, because the streamlined electronic submission process takes a lot longer than the old paper submissions, which just had to be in the hands of the courier by midnight on the due date.)
These dates work out well, because I won't have to tell CIHR all the details about the megabucks we're asking NIH for (you have to include with your application a copy of the summary page of any related proposals you have submitted), but can just casually mention that we plan in the future to apply to NIH for sequencing money to address related questions. This is good because Canadian grant panels aren't always comfortable with giving their limited funds to people who have lots from other sources. They also may not be happy if they see that you have already applied elsewhere for funds to do overlapping work. But NIH doesn't mind (see my previous post), so having already applied to CIHR won't faze them.