Disclaimer: this is only regarding my experiences at both stores. I've not been to every Walmart/Target in the world, but odds are that you've never been to my local Walmart/Target either.
I prefer going to Walmart instead of Target every time and for any sort of shopping. Walmart still has the sort of atmosphere of being a classic superstore that carries actual brands and has some image of option or variety. Everything at Target seems to be house brand and overpriced at that.
Most criticism about the Walmart shopping experience seems to be thinly-veiled classism and most pro-Target arguments are just "I don't have to be around the poors." Neither of these appeal to me and I find the atmosphere at Target to be overbearing, uncomfortably sanitized, and their security policies are invasive, to say the least.
I don't care about the politics of either company. If I'm shopping at a fuckhuge superstore anyway, I'm probably in a rush and need whatever I'm there for that day. Neither store is ever my first choice (or second, third, etc.), and if I can, I'll source whatever I need locally/used/or online, but if my only two options are Walmart or Target, I'll go to Walmart every time.
FWIW I thought for sure that Target had stores in Canada, but you're right that they only operate in the US. Walmart has stores in 19 countries, though. I think my original statement still applies.
We had Target for just over a year. They opened a bunch of stores and crashed and burned because the prices and experience weren't even comparable to what they had in the US. It's now a case study in how not to expand your business.