To make comparisons convincing, one needs sufficient similarity of context and dynamics to make deduction, at whatever level of abstraction, valid.
UCLA rose to power with a team of 4 year guys under 6-6 and with less overall talent than several other programs.
UK has since Cal's arrival, boasted sharply more OAD/TAD talent than other teams.
UCLA's early champions involved very little recruiting at all.
UK's first champion under Cal involved heavily systematized recruiting.
After two rings, when Sam Gilbert entered the UCLA scene and reputedly began helping UCLA recruit via reputedly illegal assistance to players, there has never been one shred of evidence indicating that Gilbert did anything but bring UCLA up to the level of illegal recruiting assistance already long found at most of the elite and major programs of the time.
UK and its advocates boast of many legal resources being applied much more intelligently by UK to achieve UK's extraordinary recruiting classes that is reputedly not being done at other elite programs.
UCLA competed during the age of the Converse basketball shoe monopoly in college basketball. There was to the best of my recollection no other shoe maker supplying shoes to teams until very near the end of Wooden's tenure. Converse offered no huge endorsement contracts to coaches, or schools, that I recall either.
UK competes during an age of a Nike dominated shore/apparel producer oligopoly of Nike, adidas and Under Armour with endorsement/marketing agreements in the millions to tens of millions of dollars with schools and coaches and with OAD/TAD players receiving multimillion dollar endorsement contracts within a year to two years of signing with UK.
Perhaps most importantly of all, UCLA won 10 rings in 11 years with rarely more than 2-3 players turning pro and 4 of those 10 seasons having equal, or inferior, talent to the elite programs in the country.
Conversely, UK has so far only won 1 ring competing with talent generally equal to, or sometimes sharply superior to other elite programs.
All of the above makes me doubt what insight can be gained in comparing Wooden's ten year ring dominance with what UK has done so far, and what UK is likely to do.
IMHO, and somewhat ironically, as UK seems to be operating in an era of larger scale talent concentrations, and effectively unprecedented Big Shoe-Agency-TV-gaming revenue inputs into the process, that what seems to be happening, based on the early results of UK operating with sharply rising and increasingly asymmetric talent advantages that, the importance of actually winning rings is diminishing. UCLA with a few dominant players--Alcindor and Walton, completely dominated the championship process for 6 years. UK with its steadily increasing stream of superior talent can only win one ring...so far. Without putting too fine of a point on it, showcasing, rather than winning rings, increasingly seems to be the function of UK basketball. And this makes some anecdotal sense. If the bulk of the incentives of college basketball lie increasingly just 12 to 24 months ahead for a team of 9-10 OAD/TADs, and winning a ring does not sharply alter the NBA contract size, or the Big Shoe endorsement size, what really matters most is getting the most season long branding and promoting exposure on TV for a 40 game season. Winning a ring would be nice, but it is hardly crucial, for a team with 10 OAD/TADs at all to accomplish the branding sought by the Big Shoe-Agency-NBA complex. But getting to the Final Four, and preferably the Finals is pretty important because it implies a lot of additional hours of prime exposure in media.
And if one were a shoeco legally supplying talent to, say, 3-4 elites, all that would really be important would be that that all four reach the Final Four, and after that it wouldn't matter a whit which one won the ring.
Or so it seems.
