I've given it some thought and I've decided to edit out the black outlines. Personally I like the look of black outlines on these sprites but I'm hearing from just about everyone that it's 'not right' and that it's not how real artists of this variety create their images.
The problem is not that it's "right" or "not right". The problem isn't even that it's "not NES". Even in NES sprites - as you pointed out - some do use black art lines (I spotted it on Chip'n'Dale, for instance), some don't, some use coloured outlines (TNMT), some have a black "outline", but no black "artline" (megaman).
The problem is to ensure that your character has:
- good readability on any of your game's background
- clear identification of its features.
The thing is, black lines draw attention very strongly. And because you're doing pixel art, they can quickly become too thick compared to the rest. They also "flatten" your overall work because they don't match the lightning: they're black regardless of whether this is a shadowed or a enlightened area. For that reason, people that want to convey volume of their characters (as opposed to cartoon-looking sprites) prefer to use tinted out/art lines because it's easier to adjust the shade you use for the line compared to the shade you use for the shape.
They won't be any issue with characters such as Mr. Trenchcoat or Mr. BigBlue. Your winston cyborg has much more features, but he's smaller than the other guys. At that scale, black art lines degrade readability. Finger and face are hard to identify. The gun and chestplate look flat because having strong black breaks the effect of close specular spots.
Generally speaking, as size decrease, artline-based pixel art becomes more and more difficult to master because
one misplaced pixel breaks the whole thing. Helm has a great theory for that, which I personnally failed to practice so far.