"I love you."
I have a guess. I think "kocham cię" puts more stress on "love", while "kocham ciebie" puts more stress on "you."
I think you're right. I just read a couple of explanations by Marek. He said ciebie is the stressed version of cię, and he remarked further that cię should therefore not be used at the end of sentences of more than 2 or 3 words. Ciebie should be used instead. I think it was he who also said on the other hand, you generally want to avoid starting a sentence with an accusative pronoun, unless you really mean to emphasize it.