Native Linux Runtime: Poor performance, acceptable battery life, frequent bugs, UI issues.
Default Proton: Good performance, basically bug-free experience in my first 100 hours. Recent update(s) seemed to have degraded performance in some areas.
Proton GE37: Improved performance and thus battery life. Speeds up game saves, loot gen, and end-of-combat tallying. Fixes recent non-GE issues with longer combats stuttering and experiencing aggressive slowdown. Improves uninterrupted walking + interacting with objects (resource nodes, etc.).

You can heavily restrict CPU and GPU to max savings options on Deck for exceptional battery life at the cost of somewhat longer loot generation and save times (more noticeable late-game).