A battle between two behemoths from the popular anime series' My Hero Academia and Attack on Titan is definitely intriguing and worth pondering. While it is highly unlikely that a collaboration between the two great anime series will ever happen, it still does not hurt to gander at possibilities.
Whenever the word "sheer size" comes to mind from the two series, the pro hero, Mt. Lady, and the Female Titan come to mind first. While the whole Attack on Titan series is based on the fact of huge creatures, still to keep it fair with the argument, let's grab the Female Titan to compare.
Disclaimer: This article is speculative theory and reflects the author's opinions. It also contains potential spoilers from the My Hero Academia and Attack on Titan anime and manga.
Clash between the two behemoths from My Hero Academia and Attack on Titan
To begin the comparison and speculate on the fight results, it is necessary to account for all the physiological aspects of both Mt. Lady and the Female Titan. While both the behemoths from the My Hero Academia and Attack on Titan share their similarity in sheer size, they have quite different physiologies, giving an edge to one over the other.
The biggest advantage Mt. Lady would have against the Female Titan is her strength due to the mass of her body. While the Titans can get big in a matter of seconds, they are not very heavy, as they are direct transformations of human beings and thus carry less weight after their transformation.
Meanwhile, Mt. Lady's quirk from My Hero Academia, Gigantification, allows her to grow and expand her body to a specific size. This means that rather than taking on an apparition of a huge entity, Mt. Lady expands her body and its mass, allowing the growth of her weight alongside her size.
Furthermore, it was a size comparison between the two; their respective series provide the exact height for both individuals. In her transformed form, Annie Leonhart, the Female Titan, towers at 14 meters, while Mt. Lady, when using her quirk, grows to 20 meters, overpowering the Female Titan.
Not only that, by Mt. Lady is taller than every other titan from the series, except the Colossal Titan. Additionally, Mt. Lady has longer legs than Annie, which will likely give her the advantage of covering more ground than the Female Titan, opening up several opportunities and possibilities of approaching the battle.
To focus on the comparison of strength, while the Attack on Titan's Female Titan is undoubtedly strong with her abilities, her strength is slightly overtaken by My Hero Academia's Mt. Lady. In the anime, Mt. Lady holds off and stalls against one of the strongest and huge villains, Gigantomachia.
Final thoughts

With every fact and comparison in mind, it can be concluded that Mt. Lady will likely be the victor if the My Hero Academia and Attack on Titan series ever merge and a fight between Mt. Lady and the Female Titan were to break out. Her victory will most likely be aided by the difference in their heights and powers, offering Mt. Lady the slight edge over Annie in her Female Titan form.
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