I've decided to do a full analysis.
Mami's stuff
Immortality (Types 2, 6 and 7) - none of which are going to help her when Darquesse atomically scatters her and her soul gem.
Magic - Darquesse analyses, copies, and nullifies.
Energy Projection - Darquesse catches and throws the energy straight back at her. Then copies it for good measure.
Weapon Creation - Unless she pulls a gilgamesh and creates a gun directly behind Darquesse, this won't help. And even then it still might not help seeing as Darquesse would just sense the weapon/magic creating it.
Weapon Enhancing - again, not going to help.
Healing (Mid level, scaled from Corbeau) - gets atomically scattered, transmuted, or erased, or just has her head blown up.
Telepathy - only via Kyubey iirc, and not combat applicable.
Telekinesis - only for her guns, and Darquesse has much better TK
Transformation - only for becoming magical girl.
Gets stronger when critically damaged - a nice ability, but Darquesse isn't going to critically damage Mami, she's going to freaking tear her into bite sized chunks.
Resistance to Magic, Mind Manipulation, Life Absorption and Status Effect Inducement - ok, some useful stuff. Seeing as all Darquesse's abilities are magic, Mami might be able to resist some of her abilities. That being said, we don't consider "resistance to magic" to mean "resistance to all applications of magic", so it's still probably not going to help that much against being atomically ripped apart or erased from existence. Resistance to mind manipulation is good though, means Darquesse can't just take control of her.
Unconventional Soul Manipulation Resistance - due to the soul gem. Honestly though, this is a major problem for Mami. Darquesse can see souls, so when she sees that Mami's is in her soul gem, she's just going to go right for it.
Statistics Amplification (Speed and Attack Potency) - nice, but Darquesse has much the same thing, becoming increasingly stronger and more powerful the longer she is "out" as the dominant personality.
Magic Detectio - does it act like a spider sense, or just "there's a magic person over there"?
Thread Manipulation - normally I'd laugh at this ability, but Mami's is pretty good. Still, I don't think it would be very useful against Darquesse.
Duplication - making decoys. I doubt they'd fool Darquesse, who can see magic and souls.
Can make her bullets explode - some nice AoE
Status Effect Inducement (Ignites enemies with Tiro Finale) - Isn't this just fire manipulation? Why status effect inducement? Either way, Darquesse just nullifies the fire or something.
Power Nullification with Ribbon Trap - Darquesse resists
Information Analysis (With Weakness Analysis) - So she knows exactly how screwed she is in advance. Wonderful. More seriously though, I don't know what information this gives, but if it tells about Darquesse's "destroy the brain" weakness, that is an advantage. Just a question of if she can actually make use of that information before Darquesse kills her.
Attack Reflection (With Gun of Aegis) - what sort of attacks? Physical/energy attacks, telekinetic attacks?
Forcefield Creation (With Absolute Territory) - how good is the forcefield? Does it just stop physical attacks, or can it somehow keep out the Black Flames (which Darquesse can just make appear on her targets)
Darquesse's stuff
Magic (including manipulation the magic of others to stop them using it or force it to activate) - yeah. Very good stuff. Darquesse could just prevent Mami from using any of her abilities, or force her to use it until she turns into a witch (not that that would be great for either of them, but Darquesse would still probably win)
Elemental Manipulation - meh
Darkness Manipulation - Shadows forming blades and tendrils and whips and shields that act on their own to protect her from threats and have enough range to cover an entire battlefield? Quite good
Flight - a tad more agility (Mami's pretty good with her spiderman swings) and can play keep away.
Forcefield Creation - very useful, considering that Mami destroying Darquesse's brain is about the only way she can put her down.
Enhanced Senses - no sneaking up on her
Able to perceive the flow of souls, magic, and energy and can replicate them - Darquesse can see where Mami is hiding her soul, sense the magical abilities she is about to use, and can copy all her magic.
Soul Manipulation - normally I'd say useful, but in this case it's redundant seeing as Mami's soul is in a breakable physical form.
Dream Manipulation - not useful
Mind Manipulation - Mami resists.
Regenerationn (Mid, capable of healing gun wounds to the head and reattaching her severed head to her body) - quite useful. She can heal any damage to herself caused by Mami's bullets as long as it doesn't outright destroy her brain. And it's done almost instantly, so it's faster than Mami's regen.
Power Nullification (Can manipulate the magic of others to prevent them from using their magic, passive or active) - very useful. Basically shuts down most of Mami's options.
Attack Reflection -
she reflects energy attacks.
Existence Erasure - if through some miracle Mami survives everything else, this will kill her, seeing as Black Flames appears instantly at the target's location.
Absorption (can absorb the energy of those she kills to grow stronger) - not that useful here. If it was Witch Mami, she could absorb the familiars though.
Can increase her density to increase her durability - fairly useful for surviving Mami's attacks.
Necromancy - nothing too fancy. Mostly just the aforementioned Darkness Manipulation. Don't remember her ever pulling zombie army stunts, or implying she could.
Telekinesis (on a sub-atomic scale) - either she sub-atomically atomises Mami, or she turns her into a rubber ducky.
Energy Manipulation - fun, but outclassed by the other stuff she has.
can "shunt" between universes - she can avoid Mami's attacks (never used it like that though) or temporarily retreat to another universe (has used it like that) where Mami can't reach if she needs time to recover.
Can reduce or shut off her own sense of pain - not that Mami has any pain manipulation.
Possession - interesting. I'm curious if she could possess the telepathic magical girls, but for now I don't think this is very useful.
Pain inducement - could possibly incapacitate Mami with pain, seeing as Mami never to my knowledge pulled a Sayaka-I-Don't-Feel-Anything-Miki.
Resistance against Magic - useful
Resistance against
Clairvoyance and Precognition - Mami has neither
Reistance to
Power Nullification - Seeing as this is one of Mami's trump cards...
Resistance to
Sealing - Mami doesn't have it.
Resistance to
Sleep Manipulation and Power Drain - Mami has neither
Resistance to
Possession - so the type 6 immortality (which I've never been clear on how it works) won't work anyway.
Soul Manipulation - Mami doesn't have it in this form, but if she turned into a witch Darquesse would straight up ignore the Witches Kiss.
Mind Manipulation (including telepathy) - oh hey, I forgot Darquesse resists telepathy. So if Mami tries to read her mind (I don't remember her doing that in PMMM, but I haven't seen any other PM stuff except Rebellion, so tell me if she did it elsewhere), she either fails, or makes the mistake of entering Darquesse's mind and gets mind-haxed.
Conclusion
So, with that done, I'm inclined to say Darquesse wins rather decisively, bordering on a stomp. Oh sure, maybe Mami could win if she sees what Darquesse can do and goes all out from the start and manages to get a headshot, but more often than not she's just going to get power nulled, power copied, and atomised.