Main reason why Final Fantasy 3 and 4 is better on DS original over 3D remake ports on PC and such

1: The screen adjustment looks nice on original DS (well Dpad is well designed for it, its not so good on DSi though
2: It uses two screen support, so it is interesting.
3: Everything that gets ported from phones always turns to shit. Which is what ports of FF3 and FF4 3D remakes started as (great handled quality on original DS hardware, only to have cheap phone copies being the ports for other devices), before it finally got ported to PC from the phone ports. Only exception of a game i liked is FF4 The After Years 3D version, because there was more original effort in production of that one. So one exception to that one
4: The interface is way better on DS original (only downside is you cant unlock all stuff in FF3 DS version due to wifi gimmick... but its better experience overall)

edit: Overall, interms of what is best DS experience? Either "Original DS or a Nintendo 3DS". (DS lite "not tested it" but it looks like it suffers from same problems that DSi has, which is the buttons isnt as comfortable as original DS is. Nintendo 3DS has one advantage which is a analog stick you can use for DS games.)

So basically, i recommend either Original DS or a Nintendo 3DS. Either of them is fine. Though i do sorta prefer the screen of original DS more than 3DS atleast.