I agree that it depends on what, exactly, you say.
I ALWAYS notice attractive people, whether they are men or women, and I admire from an aesthetic standpoint whichever features make them most attractive to me. I have been known to compliment people on their eyes, their hair, their teeth (I absolutely LOVE a beautiful smile on anyone), their clothing/shoe choices, and (especially) personality traits (empathy, attention to detail, tactful communication, quick wit, excellent insight, humor, etc.), but I always make every effort to be tactful and sincerely respectful. This means I won't shower people with a barrage of compliments but will choose one or two things that I think would mean the most to the person complimented. For example, if it is obvious that someone puts a lot of effort into grooming his/her hair, then presenting a polished and groomed appearance is obviously important to him/her, so if I think his/her hair is gorgeous, I will tell him/her so. If s/he is obviously a careful dresser and I love his/her shoes, I won't hesitate to tell him/her. And if I really think so, I will tell him/her that the entire outfit looks nice.
But I try to be mindful with compliments because I don't want people to feel uncomfortable or feel as though they are being ogled. If a person EVER shows any sign of discomfort from receiving a compliment, I would take that as a cue to back off and be more formal and respectful.
The most respectful and thoughtful compliments are those that show appreciation for a person's core being: his/her tastes, values, insights, and choices/actions. Telling someone that s/he is an excellent parent, son/daughter, or friend is perhaps the most meaningful of all.
Even though I am straight (or perhaps I should say BECAUSE I am straight and in a committed marriage), I am much, much, MUCH more likely to compliment a woman. I usually just keep my opinion about a man to myself rather than risk being perceived as coming on to him.
My compliments are always G/PG-rated though, no matter who I compliment, because anything more than G/PG-rated DOES come across as a sexual advance. And any compliments that could be construed as a sexual advance are reserved for actually USING them as a sexual advance! Since I'm monogamous, my husband is the only one who receives those kinds of compliments from me.