I've noticed that fans tend to have a strong preference for one theme or the other, and I'm just curious what people's reasons are for their preference.

I know I personally prefer the theme of romance because of its fantasy element. The idea of a grand epic involving princesses, forbidden love, mysterious gems powered by emotions, and romance on a galactic scale just gets my creativity and imagination going. XD;;

Personally I'm going to have to say I prefer the friendship themes more.  The romance is good and I have my favorite couples but romance can be very hit or miss depending on which version of Sailor Moon you're watching or reading.  But other than maybe Crystal, the friendships are typically always very solid and strong and it just makes you wish you could be friends with the Sailor Soldiers too even if you didn't have any special powers.

i like both themes as long as they don't play up either one of them too much without expanding on the other

But i've always liked the friendship between the Senshi. They're not friends just because they have to be they actually share a strong bond with each other in most versions of the series

That's one thing I love about their friendships, especially in PGSM where you actually see them have to make their friendships work.  It's not like the anime where everyone has this sort of set role but like sometimes they don't see eye to eye with each other and sometimes they have more of a deep respect for each other than an OMG best friends type of relationship and I loved how it portrayed it in a way that was messy yet beautiful and touching at the same time.  PGSM friendship just gives you all the feels all the way.

Well I myself happen to be a huge fan of romance. The only reason I started watching sailor moon was because of the relationship between Usagi and Mamoru. It kept me more interested on how it would play out.

Friendship. IRL, I try to be a champion of discussing other types of love beyond romantic partners. Sailor Moon has always a shining example of a story where this was such a prominent theme and probably helped instill such beliefs in me.

Friendship. But don't get me wrong, the romance was great too but I like the friendship the Sailor Senshi had with one another, it was like a sisterhood of some sort. Their friendship with one another and their devotion to their princess was my hook.  

I'm not a big fan of romance in general, and the romance in SM was kinda forced at times, so I prefer the friendship themes.

^^same. Though if it's a gradual buildup and done well, I enjoy romance on occasions.

For me it's romance

It's a shame though that these two themes are believed to compete with each other, instead of supplementing each other.

If I HAVE to choose one, I'll go with romance. I'm very cynical in real life and in my past I've found that while people are very "yay, the power of friendship!" when they're single, many of them tend to forget all about their friends and stop caring about them or wanting to see them once they get into a romantic relationship. Or when they do meet the friends, all they can talk about is their relationship. It's not everyone, of course. But too many of my friendships have been soured when my friends completely stopped caring that I existed because now they had something else to hang on to. So over the years, I've come to perceive romance as something more "solid" and where a partnership and emotional support were better guaranteed, than in a friendship. The chances of my SO forgetting that I exist in favor of someone else are far smaller. Cynical? Very much.

But this is just what I'd choose if I had to choose one or the other.

Personally I would add a third theme and choose that one instead: being strong on your own, without having to rely on outside help. I think it's very important that we learn to be as happy and strong alone, as we are in the company of our friends and/or SOs. It's not okay to judge your life by the existence and nature of certain relationships. You are your own person, and it's important that you're at peace with yourself without mention of outside influences... And Usagi pretty much has to face her fears and enemies on her own at the end of each arc so... I think the theme is represented in the story  

One could even go further and say through Usagi's friendship, the Inner Senshi all learn to love themselves and be self-sufficient, rather than insecure and lonely.

^ Very good point! And they see how personality traits that they once thought were flaws, can be their greatest qualities if used correctly and completely accepted