I've found there to be great inconsistency in fingering suggestions. I've seen publications where the LH is 4-2-1 and then the RH, on the same key spacings, 3-2-1. Personally, I work with my student's hands to discover which works best for them, but constantly mention to them that as they grow older, they will want to experiment with other fingerings, looking for fluidity, each of movement, etc.

Just wondering how important this is.

I still think the best approach is to let the hand decide which is more comfortable. When teaching, simply watch the student, and suggest to the student to use one, then the other, observe, make a suggestion if one is obvious more relaxed and/or stronger than the other.

Try this,Open your hand to the shape of an octave. Now which finger is closer to the note a third below your pinkie. I'll bet it's 4. The 3 fingers in the middle tend to stay together. To use finger 3 you have to enforce an opening between fingers 2 and 3. I believe that is why 4 is the appropriate fingering, because it is a more relaxed, natural hand position.

Try this,
Open your hand to the shape of an octave. Now which finger is closer to the note a third below your pinkie. I'll bet it's 4. The 3 fingers in the middle tend to stay together. To use finger 3 you have to enforce an opening between fingers 2 and 3. I believe that is why 4 is the appropriate fingering, because it is a more relaxed, natural hand position.

I need to clarify-
I was referring to white note, 4 note (or more) arpeggios and chords. Ex. L.H. C-E-G-C
When there is a black note in the middle, then 3 is the correct fingering.

Our hands are so vastly different - in size, stretch, strength, etc., that to say there is "one correct fingering" for each passage, be it an arpeggio or anything else, is, IMO, quite risky for a teacher and student. I have 5 or 6 different sets of major student works, accumulated over many years of teaching, and none of them agree on fingerings. A fairly recent UE urtext edition of either the Mozart K545 or Beethoven Op 49 (I forget which, sorry), offered really unique fingerings, yet, I could immediately see some of the advantages to students using and learning them. Overall, I'm probably much more tolerant of students using the 3rd finger in arpeggios because my own hands, though large, do not stretch well between fingers 3 & 4. I get much smoother playing sticking with the 3rd. But I have students who can use the 4th, and do so just as well as I can using the 3rd. For them, the 4th is the better choice.

I'm with Gary. Everyone's hand is different. What works for me may not work for you. My basic technical premise is to keep the arm aligned behind the hand via the wrist. You have to always look at the proportions of the fingers to each other.