I drain the bacon grease until it's just covering the pan, hardly dripping at all. Then I fry the eggs. I use cast iron, which works particularly well for this sort of cooking (though butter does make the eggs stick a little less).
Butter actually contains more saturated fat than bacon grease, though it is true that grass-fed (pasture) butter has tons of good stuff for you, and should be the butter of choice for Paleoites. You should have little trouble comparing 100g of bacon grease to 100g of butter nutritionally, and you'll find they're mostly comparable, with the slight edge going to bacon (slightly less cholesterol, sodium - if using salted butter - and sat. fat).
My advice, if you've got the bacon grease hot from the bacon, fry your eggs in it. It's not any worse for you than butter, despite what many of us have been told. Use butter when you don't have the bacon grease or are looking for a sweeter, obviously butterier taste.
Despite loving coconut oil and using it all the time, I have trouble frying eggs in it. Probably user error.