There's not really that much difference, although using their contraction form would sound more natural. However, is 'is' a much better word to use if you won't use their contraction form.
For example,
In American English the phrase "gone to hospital" would not/wouldn't be correct. One of the articles, "the" or "a", would be necessary.
and
In American English the phrase "gone to hospital" is not/isn't correct. One of the articles, "the" or "a", is necessary.
- Would is used to communicate about a hypothetical or an imagined event, and it is frequently employed when that prospective circumstance will or will not occur. While is is classified as a kind of verb where it indicates occurrence or a state, or rather just simply a linking verb.