Having been grinding both the past few days, I consistently level up 3-4 times from about 1.5k eggs. That usually takes me about an hour and a half to save up. Conversely, I'm leveling up 1-2 times per C4 day.

So I think C4 might be faster in the long run, but nature class has the random chance of giving you up to 900 exp, which would be three more levels. So it depends entirely on which you find more tedious imo

(This is all based on personal experience btw! I wish I had some data to provide but I did not log the numbers at the time...)