I wasn't exactly sure how this would play out, so I wanted to check with the experts.

Player A attempts to recruit an equipment to his char.

Player B responds by stunning the char targeted by the equipment.

Player A allows the stun to happen, then recovers the char.

Now when the equipment tries to resolve it's attachment, the char is a legal target. But of course this is assuming it is treated as the same object. So, does the equipment successfully attach or does it return to the owner's hand?

A character that stuns and recovers is definitely the same object---among other things, that's why Quicksilver keeps his pumps after Luna recovers him. The target's legal, the equipment attaches.

And if the target of an equipment recruit effect is illegal, btw, the card doesn't return to hand; it's put into the KO'd pile.

I believe a card only "forgets" that it's a particular object if it changes zones. I don't have the rule citation for that, but I believe an appropriate example of that principle would be if you had Oracle out, used her to draw a card, then returned her to hand (via Swift Escape or some such), then put her back into play (recruitment or substitution)...you could then draw a card with her again since she's considered a different object than what was out earlier, allowing you to (sort of) circumvent the once-per-turn rule on her card. So I guess that if the character-to-be-equipped were returned to hand, then put in play, then the equipment would no longer be targetting the same object and it would end up being KO'd instead. Stunning a character doesn't make it a different object (or else Oracle could be REALLY abusive with the right strategy and cards), so the equipment recruitment you've described would successfully resolve.