If you want to increase endurance for running I think the general suggestion is to hit the track and do running? Get your mile time down or similar.

In my personal experience I've found strength training better for losing weight than just cardio but any activity will help a bit. You'll really need to adjust your diet in some way for it though, or at least start counting and keep your calories steady as you do more activity. Trying to outburn what you eat takes like an hour of exercise a day otherwise, it's tough.

Strength training has more of a positive effect on body composition.

The problem with doing a lot of cardio is that you need muscle to burn calories (especially so without injury and as you get older), and too much medium intensity cardio will start to chew up lean mass.

No harm in doing a bit of both though, especially if your goal is fitness/maintenance rather than maximum strength or a particular look.