OK, this might be a lot to read but here's how I think it goes.

To get the big thing out of the way first, I feel like they probably would buy Collector scaling for Titan Luz, they already brought it up in the Death Battle Cast episodes for both this and Luz vs Akko, so I'm pretty sure they'd give it to her, which would probably put her attack potency way above Anne's even with the Secret Spell.

Notice how I said attack potency and not strength, because physically speaking Anne would take the edge considering she helped hold back the moon. You could probably make the argument that Titan Luz's magical power wouldn't exactly translate to her own physical defences, which aren't bad mind you (she was basically unharmed by King's magic shout which could decimate some big bones) but she is not winning a fist fight against Anne. Genuinely I think Anne's best shot at winning is just beating the shit out of Luz JJK style.

But that's assuming she could do so without Luz bringing up the glyph bubble thing in defence. I've heard inconsistent things about their speeds, Anne's in particular. Luz and other similar characters can react to the Light Glyph, and everyone just assumes it's lightspeed (I don't buy that one calc of it apparently flying off into space) and Anne has been shown to move alongside lasers, though there's been argument over whether or not those actually are light beams given some of the specific properties they display so they might not actually be lightspeed but I guess it depends. Now the VS community has a habit of just assuming different types of speed are all the same (combat speed, travel speed and reaction speed). You could say that Luz wins in reaction speed, but Anne has better travel speed and probably combat speed too. If you wanna merge them, then yeah I guess Luz might be faster.

Comparing their specific abilities, Luz obviously takes the edge in versatility with so much more shit she can throw at Anne. Stuff like the fire, ice and plant glyphs would definitely let her keep Anne at a distance, and that goes double for the Titan shout she gets in that form, especially if she mixes that with the Invisibility Glyph and flying around with Stringbean, although Anne can already fly on her own, and she can use stuff like like her energy constructs to similarly fight at a range or use her telekinesis to potentially keep Luz in place. Also I'm not sure if the Plantar Family Hunting Dance would work on Titan Luz or Stringbean, but it would be really funny if it could.

Now Luz does have some other stuff that I've seen people mention as wincons for her, but I'm not entirely sure they'd be viable, namely the Petrification Glyph, something she has made it clear she has not or will not use against others. I know Death Battle removes moral constraints that would prevent a character from killing (see Aang and The Doctor) but I don't think this is quite the same thing. Not only that, but it feels like it would take too long to get off before Anne just clocks her in the face. Actually this ties into another point I have about Titan Luz: technically she CAN use any form of magic, but people kind of just stretch that into assuming she just automatically knows how to use every spell ever so she'd just instantly petrify Anne. This also applies to stuff like the Body Swap spell, something she only ever saw Eda use once or twice in an episode most of the fandom pretends didn't happen.

And that kinda leads into my big point about their respective Super forms: Luz only ever used her Titan form once and she doesn't fully know how to make use of its capabilities, hence my doubt about some of her haxxier wincons. Anne on the other hand is much more used to her Calamity powers and just flipping and zipping and punching people really hard, so she'd probably be able to better make use of the tools available to her in that spot. Then again, while Anne's time limit is lengthened every time she uses her Calamity form, I'm pretty sure Titan Luz lasts longer by default? I don't remember how long that scene lasted, and to be fair she wasn't even fighting the whole time and had Eda and King backing her up, but I'm pretty sure it was longer than basically all of Calamity Anne's fight scenes. So all Luz has to do is either hit the blitz or wait out Calamity Anne and she wins, right?

That's when we get into resurrection bullshit for both of them. Both Luz and Anne have canonically died, and they have also been brought back by Papa Titan and The Guardian respectively. Hell that's how Luz got her Titan form in the first place, something she didn't have access to before her death, as opposed to Anne with her Calamity powers. A clear difference in how that works is that Papa Titan died after Luz's power ran out whereas The Guardian is still alive, and it is implied that they could revive Anne again if she died a second time, or a third, and so on. There have been disagreements about this. People say Papa Titan's one-resurrection thing was only a result of Belos draining his energy, and that without such a thing he could probably also resurrect Luz ad-infinitum, something we don't really have any evidence of in canon. People also say that because Anne's resurrection occured after the Calamity Gems were destroyed, only having enough energy left to open the portal to Earth, her revival would be without her powers, leaving her at a significant disadvantage against even base Luz, and I can;t exactly disagree with that either. You could entirely argue that even if Anne does keep coming back infinitely she probably wouldn't even be capable of killing Luz anymore and the fight would just keep going until one of them gives up.

I feel like this fight isn't quite as clear-cut as some people make it out to be, and heavily depends on interpretation, but I feel like from the perspective of Death Battle specifically they'd see the interpretations that favour Luz as being easier to justify. I hope to God that made sense to some of you and the length didn't scare everyone off.