All depends on your goal. If you want to lose fat, believe it or not, in the long term strength training is the best. Cardio is great for the first while, as the progress will be more noticeable and immediate. After a bit, though, your body gets used to the level of effort and stops responding. Your progress halts and you get stuck on "the plateau."
Strength training keeps the intensity increasing. If it gets easy, throw another 10 pounds on the bar and immediately its hard again. Sure you can add a mile or a few Km to your run. But now you just extended your work out to 45 minutes instead of say, a half hour. Before you know it, you're at 2 hours of running to get the same effect that a half hour did.
Believe it or not, properly done strength training has enormous benefits for the health, sometimes on par with cardio.
As for bone health, strength training is definitely the way to go. Lifting heavy loads will stress your bones and build them thicker and stronger, just as it does your muscles and connecting tissues.
So long post short - I choose strength training. Just be sure to work on the 3 main compound movements (Squat, Deadlift, Benchpress) and once you master those with proper form, you can spread out and add other exercises. Yes even women should practice the 3 compound movements. Enjoy :)