Why not both? I have a home gym for weekdays and gym membership for weekends.
Granted, my gym membership is $10 a month ($20 for both) and then they charge $15 a month for unlimited gym child watching. Usually my wife will go to the gym during the week and drop baby off. I use it for the machines I dont want to buy and have at the house (treadmill,elliptical, pulldown machines, ab machines,etc).
My home gym has been one of my favorite discretionary purchases. Bought a cage, 300lb weight set, bench, and horse stall mat and I have been killing it 3x a week in there.
It's pretty much my only hobby. I do powerlifting though, works for me (Bench Press, Deadlifts, Overhead Press, Squats, Rows,etc).
I probably should cancel the membership, but its nice to hit some of the problem areas I miss when I am at the house.