I have an elliptical/bike at home, along with a rower (that's not currently set up as there's no room) and a balance ball and free weights. I also have been going to a gym lately. I have to admit, I like having both. At the gym, I get to try a range of equipment, can talk to trainers, and in particular I like taking classes. In addition, if I go to the gym it means at the bare minimum I'm getting in 60 minutes of cardio, which rarely happens at home. The home equipment is nice because I can use it whenever I feel like it and don't have to shower in public, heh.
I think ultimately, it's what makes sense for you both financially and in terms of what you'll actually use/stick with. Sorry I can't be more definitive.