Truth be told, you could also play it in English on its Japanese release about 1 month ago, but I personally only buy/collect the North American versions because I'm anal like that.
Anyway, Final Fantasy IV has been re-released quite a number of times, for the PS1, GBA and NDS respectively. So why should you get this version now? Here are 4 good reasons.
The Complete Collection isn't just FF4. It also includes its sequel, The After Years, that was released on mobile phones only in Japan and as WiiWare everywhere in 2009. If you don't own a Wii (and there's many reasons why you wouldn't) then this would be your first chance at playing TAY. In addition, theres a special new Interlude episode you can play that links the original story with its sequel.
This version of FF4 comes with gorgeously reworked 2D sprites. As I like to call it, it's HD2D (high definition 2D) and basically the best the game would ever look in 2D. Being in 2D is good too because it stays closer to the original feel of the game which was what made it this good to begin with. This isn't to say 3D isn't good. I simply believe that if you want 3D, you should go 'all-the-way' and hit a certain graphical standard, instead of the hideous subpar 3D graphics available on the Nintendo DS.
Just so you know, you can still play in Japanese for the NA release too.
The Complete Collection acknowledges nostalgia. While it does have a reworked script, it also stays closely to the original with its portrayal of events in the game. In addition, they give you the option of switching the game's music between the classic original, and the version that was mastered for the DS remake.
It's Final Fantasy IV. Other than being the first in the series to feature the ATB, characters with pre-assigned classes and cutscenes during battle, it is also a game that defined its genre. Without FFIV, RPGs wouldn't be quite as story-driven and melodramatic as they are today, with a stronger focus on character development and storytelling.
So if you haven't gotten it, get it now.
And if you don't have a PSP, buy a PSP and get it now :p