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?
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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".