The best replacement for large eggs is extra large eggs.

The best alternatives to large eggs are rated as following:
★★★★★  extra large eggs
★★★★  medium eggs
★★★  jumbo eggs
★★  extra large
★★  large eggs
★  jumbo
★  regular eggs
★  small eggs
  2 large eggs

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Speaking about large eggs, one probably shouldn't forget about large eggs.

Other search terms related to large eggs and their ratings are:
★★★★★ large eggs
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large eggs
extra large eggs
medium eggs