The question suggests there's a trade-off between love and honor, but this is not really true. For example, like Christianity, Islam teaches children to honor their parents and family.
Abu Huraira reported that a person said: Allah's Messenger, who amongst the people is most deserving of my good treatment? He said: Your mother, again your mother, again your mother, then your father, then your nearest relatives according to the order (of nearness). -- Sahih Muslim 2548 b
Indeed, severing ties with one's relatives is major sin 9 in Al-Dhahabi's Major Sins [pdf].
My impression (as an Islamic convert) is that love to plays a slightly different role in Islam than it does in Christianity. We definitely have love, and it's encouraged:
Love in Islam is all-encompassing, comprehensive and sublime, rather than being restricted to one form only, which is love between a man and a woman. -- IslamWeb fatwa
However, in Islam, love feels more calculated. Husbands and wives both have rights and responsibilities. Parents and children both have rights and responsibilities. Generally, we try to avoid the kind of "puppy love" that can lead to mistakes and haram (forbidden) acts.
Overall, I would say the degree of love one feels is more of a personal matter than Islamically prescribed.
I think that many Muslims consider 'honor' to be a great virtue. If a woman brings shame to a family, her brother might kill her.
This is a cultural problem in some areas, applies in non-Muslim cultures (Google
[religion] honor killing for examples), and the direct opposite is taught in Islam.
Arrogance is a major sin in Islam (major sin 17 in Major Sins), and
Murder is a major sin in Islam (major sin 2 in Major Sins).
Wikipedia currently quotes:
No Muslim scholar of any note, either medieval or modern, has sanctioned a man killing his wife or sister for tarnishing her or the family's honor. -- Jonathan A.C. Brown
To the contrary, Islam teaches patience and forgiveness.
While sharia courts can prescribe punishments, such as the death penalty for adultery, (a) Islamically, it's done through officially processes (not your brother), and (b) it's no more about honor than the death penalty in the USA is (your opinion may vary).