Plenty of great advice already on this thread. Most answers aren’t black and white. If I had to have a client do only one of these types of training, it would have to be resistance training. As people age, their muscle mass and strength constantly decreasing, albeit at different rates. Strength training will help you avoid decreases in lean mass, as well as burning calories at the same time.
I’ve had great success personally by strength training 2-3 days per week and just walking on off days. As many people said before, diet is the most important factor in losing weight. Strength training is important for maintaining muscle mass and improving function. Cardiovascular training can be important for heart health and functional endurance. I know that this is a very simplistic way of looking at things and that strength training can be beneficial in cardiovascular health as well, but that is just how I justify each method of training.