I don’t have any data on the energy usage of one versus the other, and I also suspect that you need to deal with both issues. I’d suggest dealing with the humidity issue first since you really don’t want to have mold in your home. Side benefits of a dehumidifier are that they also slightly warm the air, and help circulate the air when they are running. So adjust the humidity first, and then add heat as needed. I suggest a quality dehumidifier if you can afford one. They cost more initially, but generally have better warranties and are designed to run longer, if not full-time.
I purchased an Aloair Sentinel HD55 and placed it in a closet under a stairwell and ducted it 6 feet into a closet in the basement to keep the noise level down. Place it on a stand and run the gravity drain to a condensate pump so you never need to empty the discharge water. If you’re going to control it with a smart switch make sure it restores to the powered-on state after a power outage.
Ideal indoor humidity is based on outside temperature. You can find various numbers that are recommended - the ones below are what I’m using to automate a dehumidifier in my basement.
Outdoor Temp / Ideal Indoor Humidity
50F+ / 48%
25F - 50F / 38%
0F - 25F / 36%
-20F - 0F / 30%
<-20F / 25%