What the two sentences have in common is that neither is correct usage. In both cases, a definite article is needed after the verb.
Accounting for this, the first sentence needs a comma after "venerable", which will effectively behave as an "and".
This is a venerable, rather magnificent institution.
This is a venerable and rather magnificent institution.
As for the difference in usage, there is little difference. I would expect the first to be spoken in a more personal, affectionate tone of voice than the second.