It's semantics:

"I did a cross-canada tour". (to me that would be continuous)

"I cycled across canada". (to me that is more open ended)

If the idea is that the tour is some kind of achievement, then I think the continuous tour is more impressive. On the other hand a friend of mine did it in one go last summer on racing bikes credit card style. I'm not as impressed by that as I am by a friend who started late one summer and only made it to manitoba by the end of the year so did the rest the following year. He was going solo and was carrying his own gear.

There are a lot of different ways to do it.