As in the question title, what is the difference between the two sentences below?
ichijikan hodo kakarimasu.
ichijikan gurai kakarimasu.
How do we choose to use one over the other?
Matti's answer is sufficiently correct, but I'd also like to add that ほど seems to have more of an implication of the translation "extent" whereas "くらい／ぐらい" is more like "amount".
In the example you gave, I'd say they mean the same thing, but to me the former sounds more like "up to one hour (and very likely to be one hour)" whereas the latter is really "about an hour".
Those two sentences mean the same thing, but the one with ほど sounds somewhat more polite. When they're used in the meaning "approximately", I'd say they're more or less interchangeable.
I learned something different: If you use ぐらい or ごろ, then you are talking about an approximation, either of a time span (二時間ぐらい) or of a specific point (2メートルごろ). But if you say ほど, it's a metaphor.
"I laughed so much it nearly killed me." But of course you didn't really die. ;)