They are both grammatically fine; they are both rather old-fashioned in structure, I think.
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HUBLOTIs "I hope you are well today" more common than the two?Yes, something like that. I must tell you, however. that I never use such a phrase. If I do inquire, I write/say 'How are you?' or 'How are you doing today?'
HUBLOTWhat phrases are more suitable for business lettersI don't think I'd use one; it is a business letter.