1. The main nutrients destroyed by heating are vitamins from B complex and vitamin C (possible loss 50-70%). (NutritionData: Nutritional effects of food processing). The extent of this effect depends on the temperature, so roasting in oil can have more negative effect than cooking in water.
2. Minerals, such as potassium, are not destroyed by heating, but they can leak into the cooking water. So, boiled potatoes can have less potassium than roasted.
- Boiled potatoes, in skin (1/2 cup, 78 g): 296 mg (USDA.gov)
- Baked potatoes, in skin [should be similar to roasted, I couldn't find]: (80 g): 440 mg (USDA.gov)
A side note: sodium partially counteracts the effects of potassium in your body, so if you worry about potassium intake you may also worry about salt intake. (Advances in Nutrition)
3. Oil slows down stomach emptying thus slowing carbohydrate absorption and therefore lowering the glycemic index of a given roasted vegetable. Anyway, this sounds as overthinking to me. From the other viewpoint, roasted foods are heavier for the stomach, so they can increase the discomfort after meals.
4. Heating disinfects foods and makes them more digestible. I'm not aware that roasting in oil would be better in this regard than boiling in water. Roasted potatoes will retain more potassium than the boiled ones, but this alone is not already a "beneficial health effect." On the other hand you may consume more calories than intended vegetables roasted on oil.
5. Cooking, cooling and reheating can increase the amount of resistant starch in the food; this would, obviously, have a significant effect only in starchy vegetables (potatoes, red kidney beans, chickpeas) rather in greens (Nutrients Review). I have not found any reliable information about significant health benefits of resistant starches, anyway.
My conclusion:
I do not consider roasting healthier than cooking in water (boiling): more vitamins destroyed, heavier stomach after meals, greater unnecessary calorie intake from oil.
