Probably everyone knows why they changed the eyes to flat colors, but in case you are one of the lucky thousand who doesn't, or however that saying goes: the answer to "why did they do that?" (and, you know, why they abandoned the idea so early) is almost certainly due to a little something called
"readability on a GBA screen"
the GameBoy Advance screen is very small. Probably the size of your palm. The image above is about 10x larger than the characters would be on the screen. Even IN the amove image, the separation between iris and pupil makes the pupils look really really small, which gives them all a kind of, dead-eyed look.
If you want readability in your expressions, in a sprite, you want the eyes to be as simple as possible, to convey as much emotion as possible, in as little detail as possible. You do not have ~5 pixels to waste on eye color. No. you need all ~6 of those pixels for the pupil itself.
Let's size this image down to the correct size - so that Mario and co are their native ~30 pixels tall.
Hopefully not so small that you can't tell... but I think that starts making it obvious why the changes were made. The top sprites are muddier, with too much detail. The bottom sprites are much easier to read; not just the eyes, but also Mario and Luigi's hands, which have lost their shadows and definition in favor of clearer and more-readable shapes.
Luigi's top sprite has an expression that reads more like worry, or fear, in a way that is almost too extreme for what I know is his "jumping up in the air in surprise" sprite. And are those his hands? what is he doing with them? ARE those his hands? but on the bottom, it's clear that he's clutching at his face, and the exaggerated shape of his legs makes the body language as a whole clear!
realism is not the most important, especially in a video game with sprites this small, and especially in a videogame in the Mario & Luigi RPG series, a series with combat famously focused on quick reaction times during special BROS attacks in battle. You need the motion of Mario's jump and Mario's fists and Mario's hammer to be as obvious as possible, or else... you have made a game with mechanics that players can't read.
so, yeah. the more you know. <3