The technology to launch someone skyward is basically identical, the technology in the craft, while benefited by more modern computing (as well as enhanced material science), also largely identical.
I really don't get your statement. The Saturn V is the most powerful machine humans have ever made. No rocket has since come anywhere close to it, despite the benefits of modern computing and material science. The Space Shuttle program killed 14 astronauts, in spite of the more modern technology and the huge steps that were taken in the decades prior.
The Saturn V sent 24 men to the moon, and launched America's first space station with technology built by people using slide rules. 13 successful launches without casualties - indeed it handled situations like lightning strikes and violent POGO oscillations. It's the only machine that has ever taken humans past LEO.
https://en.wikipedia.org/wiki/Apollo_1
Arguably not a launch, as it was a rehearsal.
Saturn V remains the tallest, heaviest, and most powerful (highest total impulse) rocket ever brought to operational status, and holds records for the heaviest payload launched and largest payload capacity to low Earth orbit (LEO) of 140,000 kg (310,000 lb).
To date, the Saturn V remains the only launch vehicle to launch missions to carry humans beyond low Earth orbit. A total of 15 flight-capable vehicles were built, but only 13 were flown. An additional three vehicles were built for ground testing purposes. [0]
So why aren't we just building more of these damn things and iterating on the (proven!) design? While we're at it let's un-mothball the SR-71 and those wicked Buick start carts! [1]
[0]: https://en.wikipedia.org/wiki/Saturn_V [1]: http://www.sr-71.org/blackbird/startercart.php
http://arstechnica.com/science/2013/04/how-nasa-brought-the-...
Comparing 13 missions to 135 missions, and trying to extrapolate from those 13 missions is disingenuous (slide rules or not) - the fact is Apollo 1 did kill 3 people (on the ground) - and almost killed another 3 in Apollo 13.
As much as I disliked the STS - it only had one launch failure (Challenger), due to operating the launcher out of design parameters (which was quite arguably a faulty design) - it had one other failure (Columbia) on reentry which is in some ways is similar to the defect that hit Apollo 13, it was basically a manufacturing defect.
The reason I say technology has not greatly changed is to compare it Orion Spacecraft - which is essentially a modern implementation of the Apollo CSM. Same technology, but with better and more advanced materials. This is no different than comparing a 1929 Model A to a 1969 Ford Galaxie 500.
If the political will was present, we could build another Saturn V Class launcher today - we choose not to, but even the replacements for the Shuttle (SLS and Constellation) have proposed reusing literal technology from the Saturn Era.
[1] https://www.theguardian.com/world/2007/jul/27/spaceexplorati...