I prefer shoe molding rather than quarter round.

Depends look you want, and skill set of trim carpenter. Because this is a case of scribe the base molding to the flooring.

Shoe and quarter round.....any!! are to disguise the imperfection of the meet: )

This looks great with a flat 4" window casing, and six inch base. Single piece both.

The real point is all trim is a marriage of windows, door style, casings /base ALL and your question is really a bit broad with not enough context.

New or existing floors? How flat is everything? Will there be gaps under the baseboards as that is typically the reason base shoe is used as it is more flexible than the baseboards.

IMO it is not a nice look and if the new floors are installed knowing you do not want shoe mold then you do not need it .IMO it just is added to an install that is not perfect so need to hide themess. My hubby did all our flooring in this MCM ranch and not one piece of shoe mold or 1/4 round anywhere .. I will say though we did anew sub floor before beginning the flooring.

It will be all new flooring & I dont believe there will be any gaps so it would be more decorative than functional,

In general I like no shoe mold or quarter round. Most new construction seems to do it without (at least around me) - it's the people who add wood floors to an existing home who tend to end up with shoe mold because they don't want to pull the existing baseboards.

I don't "hate" the look with shoe mold, it's just not as clean to my eye. It is all personal preference.

I did find one tiny added bonus of quarter round though. I bought a house which has quarter round, and the one nice thing is that it keeps furniture off the wall just a smidge. End tables and whatnot don't end up knocking into the wall at all. I have rambunctious dogs (and an occasionally in-elegant SO, ha ha), and it's nice that furniture doesn't end up marking up the drywall during their games. :) The quarter round acts as a perfect spacer!