That's a question that's hard to answer without more perspective. But consider...
Both the R and S isomer of omeprazole have activity at the H-K-ATP receptor, with the S isomer obviously having more affinity. Thus, one could reasonably conclude that at worst, a 2X increase in Omeprazole would cover Esomeprazole. (I.e. 40mg racemic omeprazole vs. 20mg esomeprazole.) In reality, I would think that it's actually a ratio less than 2:1. Perhaps 1.66:1. But to my knowledge, I'm not sure a receptor-isomer focused pharmacodynamic study hasn't been done yet. If any student out there knows of one, do post.
Now in a SPECIFIC case, it is hard to know what is needed without the history of the patient. Has the patient failed therapy with only 20mg of Nexium? Did the patient just start out at 40mg of Nexium as initial therapy from their physician? If they failed 20mg and bumped it up to 40mg, then it may take at LEAST 40mg of omeprazole to even think about covering it. Likely 60mg or higher. Now based upon my subjective experiences, the majority of people taking that much Nexium just started out at that dose as initial therapy. I would tell the patient to TRY the 20mg omeprazole and see what happens. You can't recommend for them to take more than that from a legal perspective because the max OTC dose is 20mg daily.
Personally, I'd see if Protonix or Prevacid was an alternative. My P&T committee substitutes 60mg lansoprazole for 40mg esomeprazole and 40mg pantoprazole. Just changing it to 40mg Protonix would probably be an easier switch off. Inquire about the inclusiveness of the patient's formulary.
But that's me.