In British English language is often used as a denominator of social standing, therefore someone who says "I should say so" instead of "I would say so" sounds like someone from a higher social class. This is nicely subsumed in this article. See the section on sociolinguistic issues.
As for saying "the meeting be held", when I studied English at university the grammatical form was termed "American subjunctive" by our British tutors, which is quite telling. In some ways other than class consciousness American English is actually more conservative than British English. Another well-known example is the American pronunciation of /r/, which the British traditionally frown upon, but it is in fact the older British pronunciation.![]()