I've been waiting for this match! Anyhow, axes beat lances due to FE Logic, so Susie wins, ze/s
Okay, let's get serious.
Undyne has done proper training and is on par with Asgore and even overthrown Toriel in one neutral ending, so she has the skill advantage. She has a Likely Class 25 Lifting Rating, so she beats Susie in this aspect as well. She can keep Susie in place with green mode although it is pointless considering Susie has projectile attacks, Green Mode still lets a person attack, and she would give her a shield to defend against her attacks due to her nature. They share equal resistance to their attacks due to how Undertale's magic works, so not much to talk about here. Also, Undyne's determination is a thing but she can't transform into the undying here.
Susie, on the other hand, has healing in form of the food items that carry around that can keep her in an okay state longer than Undyne. She's capable of mid-range attacks so she can play keep away from Undyne although I do see Susie as the type of person who would fight Undyne head-on. If Undyne's Class 25 Lifting Strength isn't accepted, they would share the same LS if her Class 10 LS isn't accepted. Her page says she has sleep manipulation, so she might be able to put Undyne to sleep if it comes down to it.
However, what pushes things onto Undyne's side is her bullet hell or danmaku; she is capable of peppering Susie with a shit-ton of spears, and while their shared resistance to soul manipulation will lessen the damage, probably, she'll be able to overwhelm Susie if she doesn't keep her guard up though I admit Susie's experience with the dark world likely lessens this from happening.
So, I vote for... Captain of the Royal Guard due to her skill advantage, danmaku, resistance towards soul manipulation, better amount of experience, and the fact that even if Susie lands a fatal blow Undyne can potentially will herself not die (and possibly turn into The Undying, if allowed) due to her determination.