There are too many variables in lat-pulldown to consider. Apart from the two positions in your post, there is also a supinated, neutral as well as pronated grip. For the sake of not writing a whole article, I'll assume we are talking about pronated grip. So let's break this down to parts:
Muscle Activation: Latissimus Dorsi ++, Biceps Brachii +, Forearms +
Close grip lat-pulldowns is the most shoulder-friendly and risk-free out of the three variations. It will not work your latissimus dorsi as much as the the wide-grip, but it will also involve your biceps brachii. Furthermore, this variation will put stress on your forearms/wrists since the weight you're pulling down is not aligned with the rest of your arms.
Muscle Activation: Latissimus Dorsi +++, Biceps Brachii +
Medium grip lat-pulldowns is the most balanced position. It will not work your latissimus dorsi as much as the other two, but it will also involve a bit of your biceps brachii. Moreover, it is a lot more friendly and risk-free for your shoulders than wide-grip. Mechanically, your arm position is in a better spot than wide-grid so this is the main reason that you can lift heavier.
Muscle Activation: Latissimus Dorsi ++++, Rotator Cuffs -
Wide grip lat-pulldowns are indeed activating the most your latissimus dorsi, but they come with a cost. Firstly, your rotator cuffs are getting very exposed and stressed, and if we add a bit of ego in the lift it can really bring a bad outcome. Also, it is very logical that you are weaker in this grip since your arm position is mechanically in a disadvantage for pulling down.
I'm confused... What should I do then?
None of the three is the most superior. My opinion is to use the one that you find most comfortable both in terms of injury-prevention and lifting progressively heavier, and stick with it. Just because wide-grip is giving a bit more latissimus dorsi activation, does not mean that you can't achieve the same work with medium-grip. In the end of the day, all that matters is having your muscles sore. One could target the lats with wide-grips and exhaust them quickly and one could use narrow-grip to do more reps while also putting some work to his biceps. Also, do not try behind-the-neck pulldowns. This variation is bad and risky.