I never palyed the PS1 version of FF IV, but I did play and finish the American version of it (thus 'Final Fantasy II US')

Compared to Final Fantasy II US, it's definitely harder. Let's see... Zeromus' Big Bang in the US version did about 700 to 1200 damage. But the GBA version of Zeromus' Big Bang can kill a character with 2400 hp in one hit, while I was the same lv as when I fought Zeromus in the US version.

And yes, teh random encounters with enemies are also harder.
In the last floors of the Moon's Core most of my characters died each battle with only one surviving. (And I was aroudn lv 57 then.)
And it seems to me the enemies and bosses have more HP than in the US version...

Oh well, at least you have the nice bestiary and music player in the GBA version.