There is no question RPGMaker 2003 is a great deal less powerful than VX Ace, for example, but it does have some strengths.
My favorite are:
1. Default battle system is the preferred type for like... 90% of people trying to make/play JRPG games. The amount of time you have/need to spend creating your own from scratch or fiddling about with other's scripts to create this functionality is reduced heavily if RPG Maker 2003 already has pretty much what you want.This was the case with me. I have VX Ace and it is an amazing, robust, extensible tool. But no need to do all that battle engine work if what you want is in the box - so I have opted to use RPGMaker 2003 for my current project.
2. More obvious/better manipulation of tiling layers.
3. The palette constraints are in some ways a weakness.... but in other ways, it sort of "forces" you into a SNES style, which is not always a bad thing.
4. Battle events are, to me, more directly intuitive to use.
5. If you are not a programmer and do not intend to become one, I figure the forum help/correspondence with people about VX Ace is probably pretty annoying in that the first and last suggestion is always to script.
I daylight as a programmer, so I don't have much of a problem with it, but after years of 2k3 development, it makes me shake my head to see people copy-pasting a bunch of scripts they don't understand to do things that are honestly very achievable/easy with Switches, Events, and Variables. Then their scripts that they don't understand break and after a couple of forum posts to no avail they give up on their game.