Which one is correct?
It's been a long time since we last met.
It's a long time since we last met.
Does the format (sentence construction) change when a specific time, say 10 years, is given instead of "a long time"?
The first one is correct. That has a contraction, which expands to:
It has been a long time since we last met.
The word "it's" most commonly refers to "it is", but it can also refer to "it has", such as the case we are looking at here.
The phrase, "It's a long time" can be valid, but doesn't make much sense in this case. For instance, "How long does it take to drive to the middle of the city during rush hour?" "It's a long time." (In that case, "it's" refers to present tense.)
That makes sense. However, to say "It has a long time since we met" definitely feels like it is missing a key component. And "It is a long time since we met" would be even more wrong, because the "long time" refers to a time in the past. (Even if we still haven't met yet, and it is still being a long time, the phrase typically refers to the time that has already passed, so it is past tense.)