Both are excellent, nutrient packed options for breakfast. I do not think eggs have a high glycemic index. In fact it’s the opposite. Nonetheless, they are packed with protein and other vitamins and minerals that’s essential for us. Oats on the other hand is a great option and my go-to because it’s so versatile. I like them both and I’d suggest to switch between them as often as you want.
I study nutrition, eggs are very good food to be apart of a morning meal because it has almost every vitamin and mineral you need throughout the day. Eggs are very good because it has protein but any animal protein should be ok for breakfast, for example bacon, eggs etc. However eggs should be accompanied by a fruit and essential fatty acids and omega 3 fats for example walnuts, hazelnuts and almonds. And to have a complete breakfast that will last you most the day it should be accompanied by a nutritious drink like green tea which supplies you with many antioxidants that help your body grow and fight disease.
I believe that oats are better. Oats are full of fibers that provides fullness, eases the insulin response and benefits the gut health. It’s good for vitamins and minerals. I always have either oats or eggs but I always lean towards oats more.