It is unlikely that anyone here has biked across north america; it will be a heck of a lot easier to bike across the US, except for the northern areas and the mountains, it will be warmer, you will have more access to bike shop (for major repairs), it will be more comfortable, and there easier roads and routes.
This is something major; you really have to know what you are getting into; it's not like you will have a fun joy ride(at least not all the time), some days you will be so tired that you will wonder why the heck you went; others you will feel so good that you wonder why you didn't go years ago.
You will also need new, well built equipment.
I can help you plan for this so give me an email at: [email protected]
I havent done it, but i know that biking across canada would be easier because there is only 1 mountain range in canada as opposed to the US where we have 2