The healthiest choice is the one you will eat. It's more work to cook both each morning than to alternate, and in the long run it doesn't matter. That said, they both have iron and protein but oats have fiber, so on egg days have something at lunch like an apple or salad, to help you poop, or put your egg on wholemeal toast. On oat days have fewer carbs. It's a lot easier to balance your nutrients over a whole day or a couple of days than each meal.

Preference is one thing but what does that have to do with being healthy? Not trying to make fun of it, just trying to understand the idea behind it.

In terms of health, it doesn't matter I don't think. You're not going to be deficient in an important nutrient by going a day from eating it (but weeks or months is another story)

So I think if you don't want to eat them at the same time, you could just eat more of each on alternating days?

Unless I misunderstood the question