If I had to take a stab at it loaded with pop psycology and half-baked observations...
I think that the similar line is that sense of loyalty. That is the appeal of a robot, male, female or otherwise. And it is the reason why people who hate robots hate them the way they do. It all comes down to that basic core thread of trust and loyalty. A robot--if you like them--will never betray you. It will never suddenly reveal it had a girlfriend/boyfriend on the side. It will never go out on a business trip and sleep with someone else. Heck, it would never even look at another girl/boy's ass as they pass by out of reflex. Robots are--and I know this will sound odd--dogs you can talk to, forever loyal to you. Anti-robot people are anti-robot because they expect robots to betray that trust in the worst possible way. They believe the futurist's loyal boxer is really a doberman that will eat your children if you don't watch it carefully. And of course, it is a different story in different nations. You are more likely to find a Terminator in America than you would in Japan.
The difference, I suspect, is because of traditional gender roles, which are engrained in the minds of people from an early age (not to mention a splash of biology here and there). Women are typically seen as homemakers, people who serve their male partners, make them good meals and soft beds. Men are traditionally seen as protectors, someone who provides a strong pillar of support and defense who will defend their honor and their lives. You can see that in the way that in the pictures Shiro provided. In both sets, the male robot is shown less as a home maker and more as a source of emotional comfort and strength. That is not to say the female robot is never portrayed as tough and defensive. But typically, it is in a paternal sort of way. In Andromeda, Rommie is always shown to be protecting her crew when she fights. In the anime Armitage III Polymatrix, the robot is quite literally defending her child. The T-X displays a strength and aggression, but it is threatening.
Anyway, that is my personal analysis. I am sure I am missing parts of it, but to get the whole thing down pat would require a few degrees and some examination of thesis work. And by that time, I would be bringing up a topic dead for at least half a decade.
And I would say the most important rule about anything concerning the human mind is that nothing applies to everyone. The human mind is probably the least predictable thing in the universe, though you can make a lot of very good educated guesses.
And getting back to the topic at hand...When you are finished cuddling Night, Shiro...can I?
"If the time should ever come when what is now called science, thus familiarized to men, shall be ready to put on, as it were, a form of flesh and blood, the Poet will lend his divine spirit to aid the transfiguration, and will welcome the Being thus produced, as a dear and genuine inmate of the household of man."
- William Wordsworth
