I was fortunate enough to have both these birds on the same log. By a bit of work, without changing anything. I got the two together to show the sizes. By comparing the two with the log you can see how much bigger the Hairy is. Beak size also. ( photo / image / picture from Kildale's Garden )
The way I remember the two is hairy= huge and downey = diminutive. Works for me I get both kinds at my suet feeder. Jerry
The downy is a sweetie. The hairy one is very impressive. I frequently see woodpeckers and find them fascinating.