I would say don't put a frying pan in the Oven, you could however try marinating the Fish in the Oil, then put it in the oven on some Tin foil, or under the Grill.
One slight problem you get with Frying, is if you have things with a bit of Fat in them, like Pork or Lamb or Sausage etc etc, because compared to Frying, Grilling allows some Fat content to drip away, any such Fat capable of being expended during cooking, gets mostly sealed in when you fry, because there's no holes or channels for it to drip through.
In the case of something like Fish, or Chicken it's just a different process, and the dripping of some Fat content, is not so problematic, as they are low Fat anyway, but Frying involves the regular flipping of the food, to ensure even cooking, without over cooking one or both sides, and then getting semi-raw insides.
Baking usually allows for a more uniform cooking method, like with Baked Potatos, you never turn them over, you prick them a few times, to create air pockets, but they stay put during the entire baking process.
Grilling requires flipping or turning too, but the Fat drip scenario comes into being, and that reduces some Fat from foods with a bit in them.
However Baking and Grilling often do take longer. if I fry a piece of Chicken, turning it over every 2 minutes, I have a properly cooked Breast inside of 16-20 minutes, but in an Oven, it would take about 1hr at a specific temperature. sitting on Tin Foil.
I can't tell you anything else about specific cooking methods, except that frying might affect retention or quality of nutrients, compared to baking, but that's not something I can say 100% for certain.