The honest version of this question is: how many months a year do you actually want to use the space? An open deck is wonderful in May and October and largely surrendered to mosquitoes from late June through August. A screened porch buys back those evenings and adds shade, but it also costs more, needs a roof structure tied into your existing one, and takes light away from whatever room sits behind it.
Budget-wise, a deck is the lower number and the faster build. The framing, footings, and railings are the same work either way; the porch adds roof framing, ceiling, screen systems, and a much more careful tie-in where the new roof meets the old. That tie-in is the detail that decides whether you get a porch or a leak, and it's the main reason porches cost what they do.
There's a middle path a lot of our clients land on: a deck with a covered section. You keep the open rail and the view over most of the deck, and put a pavilion or a roofed portion over the seating and grill area. It's cheaper than screening the whole thing and it covers the two problems people actually complain about, which are sun at 4 p.m. and rain that ends a cookout.
Whichever you pick, the framing is where the money should go. Footings below frost line, a ledger that's flashed rather than just bolted, and joist spacing matched to what your decking manufacturer requires. Composite boards sag between joists that were spaced for pressure-treated lumber, and that sag is permanent.
One more Southern Maryland note: if you're near the water, spec the hardware as carefully as the boards. Salt air eats standard fasteners, and a deck with good boards and failed connections is still a failed deck.