Just for starters, I'd like to put out there that I am biased for Luna's side however, I tried my hardest not to let my bias influence my prediction theory.

1. The Internet's Stance

Whatdoestheinternetthink.net is a website that analyzes every single article, video, and forum post about whatever topic you type into the search box and deems how positive, negative, or neutral the Internet is about said topic by scanning the sentences and seeing whether said topic is used in a positive or negative context. I have searched both "Princess Luna" and "Rarity" and have come up with these results:

Princess Luna

Rarity

As you can see here, the Internet is mostly positive for both, however, Rarity has a much greater positive percentage than Luna. HOWEVER, Princess Luna has about 48 thousand positive hits and 65 negative hits while Rarity only has 888 positive hits and 108 negative hits. So in fact, the Internet is actually a lot more positive towards Luna than it is Rarity.

2. The Brony Fandom

One thing that makes a character likeable is how easy they are to relate to. Let's analyze some of the qualities of both ponies.

Princess Luna

-Reserved

-Calm

-Kind

-Fun-Loving

-Can be rather awkward

-Faces rather long term mental conflict

-Absorbed (for the lack of a better word)

Rarity

-Sisterly

-A Perfectionist

-Kind

-Artistic

-Superficial

-Faces temporary mental conflict

-Dramatic

Looking at these qualities, it is time to compare them to the overall MLP community.

Here is where I got my evidence: http://www.bronystudy.com/id1.html

It looks like bronies tend to be more reserved than the majority of people, who are non-bronies, which assumes a big boost in the popularity of Princess Luna.

However, bronies tend to also be more friendly and compassionate towards others, seeking harmony. This would apply to both ponies. as Princess Luna was obviously looking for harmony and friendship with the citizens of Ponyville in Season Two Episode Five and Rarity is the element of generosity and close friends with Twilight and the other 4 ponies. This factor is leaning more towards Rarity's side, in my opinion.

The brony fandom is also more artistic than the majority, which could be another factor. There is a lot more Luna-themed drawings and songs than there are of Rarity (citation needed) which could mean Luna appeals a lot more to the brony artists and composers. But then again, more fanart doesn't necessarily mean more appeal. Or does it?

3. Rarity's Huge Advantage

Rarity, being part of the Mane Six, has A LOT more screen time than Princess Luna, which exposes her personality much more than Luna's. This allows for a higher chance of a person relating to Rarity rather than Luna.

Not to mention, the "Mane Six Bias" is very obvious in this competition. Most often when a Mane Six character is paired up against a secondary or background character, the Mane Six character wins. However, this only happens often and not always. To put this into perspective, if you are familiar with the Hunger Games series, who is your favorite character? If you are like 90% (citation needed) of the Hunger Games fanbase, you said either Katniss or Peeta, and not a secondary character like Cato or Thresh. Even if that 90% factor is not true, you could probably bet that there are a lot more fans of Katniss than there are of Cato.

Rarity's fanbase also gives her a huge advantage, with her fan club having over 17,000 posts and over a quarter million views, overshadowing Luna's fan club with a measly 1.3 thousand posts and about 50,000 views. However, this could just mean that Rarity fans are more extroverted and post more often than Luna fans do.

Overall

Overall, I believe Rarity holds the advantage over Luna, just because of the immense strength of that Mane Six Bias. Although Luna is a very charismatic character, Rarity just flat-out has more popularity than her. But I still do believe that this will be a very close match, and there is a decent chance of one passing the other towards the end of the final round.