Space X's Rocket, Starship is going to have 33 engines in the first stage and 9 in the second stage producing around 80MN of thrust and could send 150t to Low Earth Orbit in theory(or so they claim) but the number of engines keeps changing(getting bigger). Saturn IV had 5 in the first stage, 5 in the second and 1 in the third producing a bit over 40MN of thrust and was capable of sending 140t to Low Earth Orbit. So for half the Thrust Saturn V could send 95% of the payload that Starship can to Low Earth Orbit, and Starship has never even proved that it can do this. The engines for Saturn IV were designed in the 50's too(but they use Kraut Space Magick I guess).
Much of this is due to how awful the design of Starship is, it's a meme con, the Hyperloop of space(or the sky so far) if you will. Additionally, I don't believe Starship will be capable of making the landing that it is planned for it. They have had trouble sending the Starship second stage only 50km and landing it, they only managed it once and for all the talk of testing reusability they never flew it again which shows what shape it was in, sending the whole thing to orbit and back and then sending it back up without severe repair is something completely different.
The Problem is the design, not only does the poor form and design of it mean that it spends more energy going up but it also means it will be under quite a bit of stress coming down. The Larger a surface is the more friction it creates and the more heat and pressure it will be subject too, the ship itself is not rigid or reinforced in anyway either while at the same time as being fat it is also long(and that length will create uneven pressure and friction), that is ALOT of stress for a hollow shell of thin steel strips to handle, the fuel within makes it little better than a time bomb as well, sure it will pressure the interior to degree but it will not be enough and a rupture may prove to be catastrophic. And that is before this hulk even hits the ground. This is a lot of money to spend on a meme.