Dude.... duuuuuuuuuuude....
She has you by the b a l l s, and she knows it. Why? Because you keep re-negging on your supposed statements. One minute you're saying you want to end things, then the next you're willing to have sex with her. One minute you're saying you'll end things, then the next she's able to persuade you to see her the next night.
You know why she has feelings for the other guy moreso than you? Because he's CONSISTENT and UNWAVERING in his dealings with her. He says he's not ready to sleep with her yet, and despite her trying to persuade him, they still haven't done it. He hits her up to hang out once a week, and despite her trying to persuade him, she's only able to see him when HE'S set the schedule for it.
THIS GUY IS DOING ALL THE THINGS YOU SHOULD BE DOING TO INCREASE HER INTEREST.
"But wait," some of the others have said on this board. "She's still giving you sex, so you're winning!" Hmmm, think about that: she can't bang the other guy, but she still wants sex... so she uses your physical body to get her release, while at the same time imagining the other guy's head on your body. Soooo... winning? LoL
Anyway... for starters, you need to be honest with yourself about this girl and if you actually WANT her. Based on the time you're spending with her and how much you talk about her, it sounds like you want to be in a relationship with her. If you do, that's fine, and you need to quit lying to yourself about it - it's perfectly okay to want to have a girlfriend you regularly bang, hang out with, get food with, etc. If you just want to bang her for a while and then kick her to the curb, you need to know that as well. But you can't be doing both - like, you can't say "I just want to bang her" one minute but then get all whiny when she starts wanting another dude.
Assuming you actually WANT her, though, you're going to have to let her go... and be BRUTAL about it.
Not brutal like saying mean things to her, but brutal in sticking to your guns. What does this mean?
1. NO MORE ALLOWING HER TO TELL YOU SHE WANTS TO BE WITH SOMEONE ELSE.
The fact that you allow this is pathetic. The proper way to handle this in the beginning would have been:
HER: So... just so you know, I like this other guy more than you, and will drop you if he shows interest
YOU: Really? Well then, let's save time and just end it now (walks off)
It's the DETACHMENT to the outcome of dating a woman that they find attractive (which this other guy is clearly showing), and something you need to show more of. It also lets her know there's a level of respect that comes with dating you, including not bragging or pining after other guys in front of you.
2. TELL HER YOU'RE NOT SPENDING TIME WITH HER ANYMORE - AND MEAN IT.
Yes, you risk getting rid of a guaranteed sex partner, but you know what? Realistically, there are others out there. And your self-respect is worth more than what she's been giving you.
More importantly, though: the fear of loss is always greater (and more painful) than the fear of gain. Right now she doesn't fear losing you because, in her head, it's not an actual possibility: you're "Mr. Reliable," so even when you threaten to leave she feels she can say a few kind words or flash a lil' skin and you're right back in. But she needs to actually feel what it would be like to not have you in her life, and the only way you can do this... is to actually remove yourself from her life. This means: no sex, no hanging out, no doing favors, no being there to talk to her when she's having a hard day... she needs to actually experience NOT being able to do all this stuff with you in order to better appreciate your presence in her life.
3. WHEN SHE STARTS CONTACTING YOU, IGNORE IT.
Not forever, but definitely for the first month. And trust, she WILL contact you. She will text you, email you, call you, try to show up to places she knows you frequent... ignore all of it. The more you ignore her, the harder she will work for your attention; the more she works for your attention, the more her brain will convince her she's doing all this because she actually likes you, possibly even MORE than the other guy who has yet to show her the attention she wants.
4. DO NOTHING DURING THE "QUIET" PERIOD
This is the point where it appears she's given up trying to contact you. Usually after a month, a woman will stop hitting you up if you've been ignoring her. At this point, she'll fall back and try moving on from you. This is NOT the time to hit her up. Continue with life as if she doesn't exist. This period may last a month or two, but usually not longer than that. After this period, she will hit you up randomly out of the blue, at which point...
5. AGREE TO MEET UP WITH HER TO "CATCH UP"
More than likely, she will throw this out there - "just wanted to see how you were doing, maybe catch up sometime?" At this point, she's gone through enough of a period without you where she really, REALLY wants to be with you. It's at this point you agree to meet up just to "chat." She'll probably give you a few updates on her life, then go into how she's so sorry for the way she treated you, and how she misses you, etc.
At this point, it's pretty easy to get a bang out of the meet-up, but it also becomes easier to talk about what you two will be going forward, and laying out the rules for what that would entail. Because, if you've gotten this far, she will be more willing to follow YOUR lead on whatever this thing is going to be, and less likely to come at you talking about other dudes she's interested in.
Of course, doing all this takes patience, and I'm not really one for trying to get girls to be with me that are expressing interest in other dudes. I'm just saying, it CAN be done, but how you're going about it will not work in the long run. Too much access + too much willingness to do what she wants never equals having the girl fall for you.