Low-intensity exercise is more effective in the short run. Since you can keep going much longer, you can (potentially) burn more calories, which (in the short run) is better for fat loss. In the long run, however, low-intensity exercise has only limited adaptive effects. That is, it doesn't make you that much fitter, it doesn't change how your metabolism works very much, but it mostly induces a one-time calorie deficit every time you do it.
High-intensity exercise is more effective in the long run. Although you (usually) burn less calories, especially as a beginner with low stamina, high-intensity training is a challenge to your body which, over time, leads to an adaptive response. The exact details are not well understood, but the idea is that your body "learns" that it has to face periods of extreme stress, and thus tries to adapt to that stress.
Just like your biceps will grow when you do lots of biceps curls, your aerobic exercise capacity (and also stress capacity) will grow when challenged. Low-intensity exercise is like doing biceps curls with an empty soda bottle: It may be enough to prevent muscle loss, but it's not enough of a challenge to induce an adaptive response. If you truly want to improve, you need to get out the heavy weights.
Since the adaptation takes a while, however, you will feel worse for a few hours or even days after an intense workout, while you'd feel better after a less intense workout. Similarly, your biceps will become weaker shortly after exhausting it with heavy weights, but that's the only way to make it stronger in the long run.
Conclusion: Low-intensity if all you want is to work off the turkey after Thanksgiving. High-intensity if you have patience and want to induce fundamental adaptations which make you stronger, leaner, faster, more stress-resistant, and so on.