"at the cost of" vs. "at the expense of"

I usually use "at the cost of", but my editor made it "at the expense of". For example, the following sentence:

The counts in Table 2 are all based on implementations that are optimized for computational cost, which comes at the cost of significantly increased storage costs in ...

was replaced by

The counts in Table 2 are all based on implementations that are optimized for computational cost, which comes at the expense of significantly increased storage costs in ...

Can anyone help explain the difference?

Solution 1:

At the expense of can be understood to be something doing damage, if you will, to the storage costs, whereas at the cost of seems to imply more of direct damage to you.

IMO you are correct.

Solution 2:

"Cost" is naturally an attribute of the relevant object (eg "what was its cost?"), while "Expense" relates rather to the relevant person (eg "at his expense"). After all, to cost and to spend are different, though related, concepts.

In your example, it may be (as suggested in the comment above) that your editor simply preferred to avoid repetition of the word "cost". Alternatively, your editor's correction could be said to have personalised the "significantly increased storage costs", depicting the storage costs as having "to pay the cost of" the computational costs.