K, if you have only 3 months to enter Canada, you should better go land before your PR visa expires. Once it's gone, it's gone. You don't have to settle right away though. You can just land and then go back home. As a PR, you may be outside Canada for up to 3 years in a 5 year period.
Then you can wait to see what happens with the US green card. If you get it, the choice is yours.
You could also go just before your PR visa expires, land in Canada, spend some time in Canada and then if you have the US green card, you could go to the US, spend some time, see how you like it. Look for jobs etc.