The HP of the monsters in the GBA version are the same as the PS1 version.

Also, you need to remember that many monsters in FFIV utilize counter attacks. This sometimes gives the impression that they're attacking many more times than they should.

Anyway, if you don't enjoy the GBA version, than just don't play it. The only reason so many people found the game to be a bit easy, is because these are many of the same people that have played the game numerous times in its previous incarnations. Also, some customization options like B-Button Dash and the ATB turn bug also make the game seem faster, but not really that much easier.

As an aside, YouTube does not make videos magically slower. The player may have had the battle speed set down as was previously mentioned, or it may have to do with the video uploader's compression methods (many people don't compress videos properly, which leads to out-of-sync video and audio and other problems).