I'll try and give a thoughtful answer. The easy reply would be to go a size or two smaller with the dropper. Size 16 or 18 nymph for a 14 dry.
However, I'll make the argument, at least for the tumbling pocket water that I mostly fish, that the size difference is not critical. I often fish larger and heavier droppers below a dry if I need to use them, with good success.
First, I almost always fish a dropper under my dry. Why? First, of course, it doubles (or triples) your chance of catching a fish, You're checking out all portions of the water column. Second, my reflexes on setting the hook on the dry are fading as I age. The dropper serves as my back-up. How many times have I watched a fish smash my dry, set the hook, and then I notice that I'm playing the fish attached to the dropper. When I bring him to hand, the dropper is in the fish's mouth, or hooked on the outside of the scissors or lip. How did this happen? When the fish struck the fly, I missed the hook-set, but the dropper tippet running through the fish's mouth then brought the nymph into the mouth and the hook stuck. Is it fair? I don't know, but it's fish on. Of course, the hook also catches them in the nose, fin or tail. That's why it's important to fish barbless.
Now back to the question of dry size and dropper size. Let's start with dry. Early season, it may not matter much because you're catching everything on the nymph. Go large with the dry, because it's just a bobber. Later, the dry starts working and size becomes important. People always say "match the hatch" but here in the Smoky's there may not be bugs hatching when you get to the stream. What size do you start with? It's always a trade-off, big works better for the angler. You can see it better in funny light conditions and it floats better. Smaller generally catches more fish. The most common dry fly I see hatching in late spring is the yellow sally, and most of these are size 18. You know your fly is too large when you start getting the "tail slap" from fish. You think he's rising to the fly, but he's really only mocking and taunting you. The lower and clearer the water, and the later in the season, the smaller I'll go. 16 or 18 is a good starting point.
For small flies to work in tumbling water, they need to be bushy and float well. Pick patterns like caddis, stimulators, and bushy parachutes with lots of hackle. Foam flies and parachute posts tied with synthetics also help. I pore through the bins at the fly shop and look for the beefiest samples of a pattern. Leave the wispy flies to the tailwater guys.
So if I get to the stream and start with a 16 dry, what size dropper? I don't worry too much. It can be a big bead-head worm or a small zebra midge. Why doesn't it matter? First, because the casts and drifts are short. When the fly hits the water, it may only need need to travel five feet or so for a few seconds in order to get through the sweet spot of the run. The dropper just doesn't have time to drown the dry. Second, the dropper is not exerting pure downward force on the dry. Cast a green weenie a watch it travel with your dry. The water current pulls your dropper along horizontally, often ahead of the dry. Your pair of flies will travel in tandem through the run before the dropper has time to drown your dry. Keep in mind this is for fishing pocket water and not still pools or big rivers.
When I take new folks fishing, I always rig them with a dry-dopper, and live with a few more tangles in hopes of catching more fish. The number one cause of the dry drowning or going under has nothing to do with the dropper. It's excess line and leader left on the water, that gets trapped by current and pulls the dry under. Once I show them how to hold line off the water and leave just the fly and a bit of tippet on the surface, or make a mend to keep line from dragging, the dry floats well and the strikes start coming.
A final thought is to keep the dry fly in good condition. I preen and take care of my dry fly more than my teenage daughter messes with her hair. And that's a bunch. If it's not floating in a bubbly riffle, my dry is in the dessicant or I'm checking that the hackles are sticking the right way. I want it to float well the first time I hit each hole, because that's the best time to get a strike.
Of course this is all subjective opinion. There are better fishermen than me on this forum that may do the opposite of these suggestions and catch more fish. That's what I love about fly fishing. We can keep learning and changing our techniques to fit the day's conditions. Sorry for the long-winded answer.