There is an old persistent myth that people trying to lose weight should work out for a longer period of time at lower intensities, because you'll burn through your glycogen (muscle sugar) stores and tap into fat. The fact is, it's your total caloric burn for the day that counts. So, at the durations you are talking about, in terms of calories burned, it's probably a wash. BUT, for cardiovascular and overall health, you DEFINITELY want to work in your target heart zone as much as you can. Even if you can't do more than 20 minutes now, you will be able to do more in the future. There are all sorts of strategies for increasing your time at cardio. For example, you could make a deal with yourself that you will increase your duration for 1 minute each session, or every other session, or something like that. Remember that if you do the same thing for the same duration at the same intensity, your body will get more efficient and actually require fewer calories than it did when you first started. One day during the week, you can add intervals to your routine, where you go hard and fast for 2 minutes, then at a more moderate pace for 2 minutes, and alternate. Another thing I do is have an extra-hard 20-minute workout one day, an interval workout for 30 minutes another, and a moderate (but still in my target heart rate) workout for 40 minutes another day. I also mix up what I do ... walk the track for the moderate workout, use the elliptical for the harder & interval workouts, even use the bikes occasionally.
The important thing is to do what you can, work in your target heart zone for as much as you can, and just work on doing a little more, gradually, over time. Also, as has already been mentioned, strength training is very important for overall health and weight loss, so if you're not doing that already, look into adding that to your routine. I actually workout 4 days per week -- cardio plus either an upper body or lower body weight routine, alternating. Then, if I have time, I might throw in a neighborhood walk, a yoga session (I try to do at least one every week), pilates, or something similar.