Neither. Hop bitterness is not extracted unless the wort is boiling, and only up to a set maximum anyway (usually 70 minutes of boiling). So, once the wort isn't boiling, no bitterness is extracted.
The hoppier beer may have higher AAU percentages- that is, stronger hops.
I don't strain my wort unless I have a ton of hops that will take up too much room in my fermenter.