Not even Sega knows all the mysteries of the Saturn. That is because of the Hail Mary Pass last move of adding an extra chip to the main board to compete with Sony, that complicated the development in order to increase potential power. Only very few games seemed to master this, in the later stage of Japanese released games. As for Dreamcast it was built on a custom version of Windows Microsoft made in partnership with Sega making it compatible with the same kinds of development tools for Windows PC, which is also why it’s a breeze to emulate. NullDC does an excellent job on most games, and it has for a while.
The actual design of the circuit was altered at a later stage where it would be difficult for Sega themselves to know exactly how to make the most of it. It’s a nuance. It is well documented that the Saturn was very difficult to develop for, particularly for those who wanted to use all its power, but outside of all the original circuitry which everybody knows that Sega knows perfectly, the part they added in the end and how to make the most of it was not found out until late developed Japanese games, by that point Sega was too focused on the Dreamcast to have been concerned with seeking documentation from those few developers, they were already moving on. Since I was into emulators and followed them closely since early on, I can vouch that solid Dreamcast emulation was available many years before Saturn emulation got to a decent level. As to my view it is based on multiple sources, accounts and first-hand testing over decades.
There’s also demand you need to consider. For instance with the OG Xbox there just wasn’t enough demand for emulation until recently, and because on the one-hand, it is very similar to a PC in architecture, it does have a custom BIOS and some other custom aspects similar to a console, meaning it shouldn’t really be harder to emulate than any other console, just that it being so powerful for its time and with little emulation demand, its emulation development has been lackluster, especially considering a lot of the people who would emulate it probably own a hardmodded one (kills your warrantee).
What I remember reading was that the Xbox’s unique BIOS made it difficult to crack, also the demand was not as high for Xbox because a lot of its popular games were on PC. Only later did people start to care about the exclusives, but most who cared early on already owned an Xbox and could even download games for free, which made emulation useless.
Hard-modded means a hardware modification, like adding or replacing a chip on the motherboard. Soft-mods only override the software. With people who never owned an OG Xbox, don’t want to buy one but want to play exclusive games, they did start to care about Xbox emulation nowadays.
Simply not enough people cared before, that’s why Xbox emulation development was slow and has only picked up recently, because only now people actually care about its emulation. This is different from Saturn where it really is more about unusual hardware and lack of documentation by Sega themselves, who modified their circuitry very late in development.
Being able to use the GPU through the emulation is only a recent development. Emulators used to have to virtualize everything in software, making it hard to emulate 3D graphics for systems like PS2 etc… it was only after this breakthrough in using the GPU in a virtual environment that emulation and virtual machines (which is parallel technology) got really good.
Before we would need a machine several times more powerful than the machine you are emulating for it to work. This is still somewhat true today, but our current professional level PCs are more than well equipped to handle emulation from the 6th console generation and before. Even though our current power PCs are more powerful than PS3s or Xbox 360s, they still struggle to emulate them because even with the ability to use the GPU, there is still a lot of software overhead in the virtualization.
There is less now that we can use the GPU but there is still much more overhead than running a native game or program developed for or properly ported to PC. It can work better with better developed and more advanced emulation, but that is usually professional level software while most emulation is made by hobbyists or research & development teams purely for experimentation. Even professional implementations are not always good.
For example Neo Geo X system is officially licensed but has problems emulating those 2D arcade classics. The virtual consoles by Nintendo themselves on the Wii, Wii U and 3DS also don’t always emulate old games perfectly. It is not so simple as one might think.