There's a large disparity about squats being bad for your knees and back. Well, there was anyway. Didn't follow that, did you?
People make the mistake of thinking that:
A) Wider grip = wider lats. This is inherently false. In fact, the closer grip will also have you working across a slightly longer ROM, which is likely better anyway.
B) Using an overhand grip is harder, so it must be better. That is to say that, since it's difficult, it's reasonable to think it's more effective. In reality, it's only harder 'cause you have less than optimal bicep recruitment, so you're losing something in the lift. A chinup recruits the lats optimally (moreso than pullups) as well as the biceps. This is why it is "easier". You can load it heavier and thusly make better progress.
The only thing I can see worth arguing is that the pullup works the lats as a humeral adductor, chinups a shoulder extensor. Big discrepancy? Probably not, but it
might have a slightly different effect. If you're a bodybuilder profressionally, maybe toy with it. Or if you're looking for a challenge in terms of leverage. Otherwise, stick to chinups.