I think they're actually similar technologies and wattages. So really I think people are comparing using a room unit (being a dehumidifier) versus a central AC systems cooling the entire house.
They can be a lot cheaper. We commonly use them in HK to stop our flats going mouldy when we are out the house and it's 35C (90-95F) at 80% humidity. It's a lot cheaper, possibly an order of magnitude, than running the air-conditioning 24/7.