After running somewhere just shy of a hundred sessions using Swords and Wizardry Complete, I find that I'm kind of hankering to go back to Swords and Wizardry Core. It's odd, but compared to the sheer amount of material I see for Complete and for Swords and Wizardry White Box, I'm surprised that Core doesn't get more love.
Swords and Wizardry White Box is actually kind of fiddly, especially in how it departs from how an increase in level also means an increase in hit die, but also in the unequal level distribution between classes, and in the various perks each class gets. There's also a loyalty mechanic unique to it, and several other instances where little variations make their way in (Haste and Slow become the single spell Alter Time, etc.). Perhaps counter-intuitively, Core is actually simpler in these respects, while the only real increases in complexity compared to White Box are that it lacks a universal attribute modifier chart and has variable weapon damage. To head off any "edition warring" at the pass, White Box is a perfectly fine game that many people seem to greatly enjoy for many reasons, and I don't have a problem with that, it's simply not the game for me, for the reasons above.
From what I can tell, the fondness for White Box and Complete over Core appears to be mainly an effect of support. White Box and Complete both have companies that seem more or less (at any given time) invested in supporting them - putting out new printings, supplements, translations in other languages, adventures, etc. Core has no such company (Mythmere Games is just Matt Finch in trade dress, from what I can tell, and hasn't put out new stuff in years, and the Swordsandwizardry.com site has been down for about a year now). That's a shame, since it's such a simple, lovely little retro-clone.