Some risk averse people are following one rule: Do not carry any electronics at any border crossing. It's a hostile territory.
I have SSD drive that I use in States. Once I'm ready to go, I swap it with "empty" drive and fire up the OS just to get some updates on files on it, so it doesn't look like it hasn't been used for a long time.
Once in Europe, I put the drive that has more tools and my files I use daily. I also use personal DropBox and the most important files are sync over the net when I login from Europe.
As to the phone - my network doesn't work in Europe anyways, so instead of selling/throwing away my perfectly working Iphone5, I use it in Europe and my new phone I leave in states.
Moreover I cannot say much about driving to Canada, but I was tempted once with saving $150 on a ticket and flying to Europe through Montreal instead of Chicago. That was horrible mistake. That airport is super disorganized and there is literally no staff to help you. No other information than to research for yourself. Few years ago some guy got teased to death because he was so frustrated and I don't blame him...
As of the phone in US, I have jailbroken version with an app that allows me to do a triple-click to shut it down completely. I got used to using this trick when I'm pulled over by LE or entering airports or other places... just in case!
I don't think I would ever give out my password without talking to a lawyer first.
I reasoned that an old Blackberry is good because there really isn't much you can do with it beyond text/email/web. And it makes me look like a tech-illiterate luddite.
But don't be mistaken, that based on the Snowden revelations, "they" may not have already had it, and needed another country's intelligence agency to access it first -- for them to get to whatever it might be, and possibly even use it against you, legally.
It's also quite unlikely that they can circumvent a basic `tar -c /dev/block/* | gpg -se ...` scheme that's trivially doable on unlockable Android phones. (Replacing the bootloader with a maliciously crafted variant that returns false partition data after bootup would work, but once again: CBSA.)
You're probably safe if you just do an iCloud backup and wipe followed later by a restore.
Certainly do replace the SIM card as soon as possible though, IMO. Unless you can verify it somehow.
"Oh, you brought an empty phone? Give me access to your cloud account. No? Ok, you're never entering our country. Bye."
How is a cell phone any different?
Asking for passwords to Facebook accounts or other information that isn't on your phone, now that's another story.
When crossing the border... backup and factory reset. Don't carry anything with you over the border you don't want customs officers looking at. I just hang onto one of my older phones to use when I travel.
When your phone is taken away after they forced you enter SU level password, you have no control of it, they do.
Whoever took it inside the room, they can:
>Browser your email, check who you contacted since you have you email box: Why you bought this on amazon? Why you bought that from Ebay? For what reason you purchase two pressure cookers from and nails from Walmart at the same time?
>Check your contacts: Who is Mr.X? When was the last time you talk to Mr. Y? What was in the conversation?
>Check what you have posted on facebook/Twitter. You supported Aaron Swartz? You are in the protest called The Day we Fight Back? What was the protest about? Who you are with?
>You may have home security Cam APP installed: Who sitting in the sofa? How many rooms do you have? Is this your wife? What is her social security number? What is her first name? On the day of Feb 21, 2013, who are the two male visited your home? What's their name and what's the purpose of the visit? How long they stayed in your house? What car they are diving? What is the plate number?
>Copy all your photos for further investation.
>Install Spyware, Copy your RSA key stored in your phone.