To him, this was hard to stomach.
To a man like him, this was hard to stomach.
To a man such as him, this was hard to stomach.
In the above sentences the words preceding "him" are prepositions, so the object form "him" is correct.
Now if you want to say 'To a man such as he is, this was hard to stomach.', that would be correct too. You would need the subject form "he" because you have created the clause 'he is'. (obviously you would not say 'him is')
It is exactly comparable to 'He is taller than me.' and 'He is taller than I am.'