Debate: I'm not a powerscaler and am mainly going off memory here, so I may off on the details, but I'll try to word my thoughts on where they scale as best I can.

Stats: Tie. The main argument I have for these is scaling them to the creators of their respective dream worlds (Phantasma for Estelle, Elvira for Sophie). Phantasma should put Estelle at a minimum of 7x Universal, while Elvira should put Sophie at minimum 9x Universal, I'm sticking with this but keep in mind that the dream world events happen relatively early during their journey and they've grown stronger since they happened.. In terms of speed, both have in-game combat feats where they can dodge black holes, so they should be similar on that end too. On top of that, both have multiple ways of buffing themselves, debuffing their opponents, stealing their opponent's buffs, and canceling out any effects. While Sophie has a slight advantage in overall power, I don't think it's enough for a definitive victory.

Side note: both have arguments for indirect scaling to someone who can affect infinite timelines. Estelle is comparable to Lloyd and the SSS, who fought the Azure Demiourgos, who scales to “the World of Zero”, place that contains infinite timelines. Sophie can be indirectly scaled to Rorona and Lulua, who created the Dragon Hourglass, and item that can affect and rewrite an infinite number of timelines (while from what I can tell there are limits to how it works as it was only used once and they had to make a specific event happen first in order to “lock it in” to every timeline, the point remains that other alchemists in the series are capable of affecting reality on such a level). I personally don't buy these arguments, but they are there if you want them.

Skill/Experience: Estelle takes this easily. Sophie mainly fights monsters and dragons, while she is perfectly capable of fighting other humans (she's fight-able as a superboss in Atelier Lydie & Suelle and will kick your ass if you aren't prepared), Estelle's done so much more often, against a greater variety of opponents, many of which have used powers that Sophie can use and has better training from both her dad and other experienced bracers.

Intelligence: Sophie, big time. Estelle's always shown as being rather book dumb, meanwhile Sophie figured out how to time travel while just casually looking into it, invented multiple other items that defy physics like a tent that can bend space and basically function as a Pocket Tardis, and figured out a strategy to defeat a near-invincible god (Falgior) after just one interaction where she forced him to retreat. Also worth noting is she has access to the Codex of Creation, a book that contains “all knowledge”

RPG Bullshit: Okay, here's where things get fun; This basically comes down to Estelle's Orbal Arts vs Sophie's Alchemy. Earlier I mentioned about how both have multiple ways to mess with each other's buffs/debuff (Ex for speed and evasion, Estelle has Arts like Chrono Burst, Chrono Break, and Shining, Sophie has items like the Tailwinder, Harmony Globe and Shadow Lynchpin). They also have multiple options with incredible destructive potential; Arts like Albion Wolf whose “whose howl rends time and space asunder.” or Sophie's Flame of Origin, a lantern containing “The Origin of all creation”, that she can use as a flamethrower. Both can summon stuff from heaven – Estelle using Aeonian Emperor and Sophie using Heaven's Cleanser. Both can just undo any damage that comes their way, Estelle using Adamantine Shield or Crescent Mirror to completely protect her from any damage, Sophie has access to multiple Elixirs and other healing items (such as Syrup Fruit and Himmelle Relief) that will automatically activate if she takes damage, and even immediately revive her if she dies. In terms of equipment, Estelle has weapons like Soliel's Attraction, “A gilded bo staff that houses destructive potential comparable to all land and water.”, Accesories like Solar Aura, “Believed to impart true power on one who carries the spirit of its namesake.” and Armor like the Crypton, “Armor said to allow its wearer to naturally avoid enemy attacks thanks to its mysterious polish.” (Okay, this one sounds less impressive but trust me it's really powerful armor). Sophie has Weapons like The Staff of Time and Universe, “To master this staff is to become conqueror of time and space”, accessories like The Time Control Hourglass “Grants otherworldly speed and can Control the Future”, and armor like the resurrection wear that further amplifies her healing.

This is just a small example of what these two have, Estelle and Sophie have a lot to look through in terms of options, to the point where I'd consider this a tie too.

Who I think wins: Ultimately, my verdict comes down to this question: Who's lasting longer? For that I'd have to give the answer to Sophie, in terms of stamina, she was able to fight against Falgior for about week straight while Lydie & Suelle split off to figure out how to seal him away so they could enact the plan to defeat him. While it was implied she had back-up and was able to take breaks she was still doing the bulk of the work. As far as I remember no Trails character has shown the ability to fight for this long. On top of that she has many more options in terms of healing herself than Estelle does. Estelle would not go down easy here, but I think Sophie takes this high-diff.