The type of potion (catalyst used, not status effect) affects how long a potion’s effect lasts when cooked into food. I don’t know which lasts from shortest to longest duration, but here’s my results for now.
I used 1 piece of boar meat and different corroding 1 potions to test this. Here’s what I have for now:
Vial
Flask
Potion
Elixir
Burst
Greatburst
Nova/Supernova
Gel
Essence
Physick
Missing: Aura (i don’t wanna spend dark sea essentia on it 
)
Incompatible: Everything else
The number of different category ingredients also affects the duration. For example, a meal with only 1 category of food (such as meat only) will have longer potion effects than meals with 2 categories of food (such as meat + fruit). Meals with more categories will have their potion effect last even shorter.