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According to the paper "Modern statistical estimation
via oracle inequalities":
‘Oracle inequalities’ are a powerful decision-theoretic tool which has served to understand the optimality of
thresholding rules, but which has many other potential applications, some of
which we will discuss.
and in page 22
An oracle inequality
relates the ...
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Since you can assume that values are missing at random, the best solution would probably be to compare both models (using F-tests, likelihood ratio tests, mean absolute error, median absolute error, or other such approaches) using the data subset that has all predictors present in both models.
Here are two other solutions to consider:
Create a holdout ...
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