I understand the basics of stock splits. My question is, all else being equal is there any benefit to buying shares prior to versus subsequent to a split? As a hypothetical, imagine Apple's price stays the same between now and their split in June. Does it make more sense to buy before June 9th or on-or-after June 9th or does it not make any difference?
Assuming you plan to buy a whole number of shares and have a maximum dollar value you intend to invest, it may be better to wait for the split if the figures don't quite work out nicely.
For example, if you are going to invest $1,000 and the stock pre-split is $400 and the split is 2 for 1, then you'd buy 2 shares before the split unless you have an extra $200 to add. Meanwhile, after the split you could buy 5 shares at $200 so that you invest all that you intend.
Aside from that case, it doesn't really make a difference since the split is similar to getting 2 nickels for a dime which in each case is still a total value of 10 cents.
There has been a lot of research on the effects of stock splits. Some studies have concluded that:
However note that (i) these are averages over large samples and does not say it will work on every split and (ii) most of the research is a bit dated and more recent papers have often struggled to find any significant performance impact after 1990, possibly because the effect has been well documented and the arbitrage no longer exists.
This document summarises the existing research on the subject although it seems to miss some of the more recent papers.
More practically, if you pay a commission per share, you will pay more commissions after the split than before.
Bottom line: don't overthink it and focus on other criteria to decide when/whether to invest.