With Murex, I initially took a "let's just experiment until I find something that works" with no fear of writing ugly proof-of-concept code. This allowed me to build a lot of stuff very quickly and originally it was written in a self-hosted git repository to solve my own problems. But as the project evolved I realised there was some good stuff in there that's worth sharing. The downside to this approach is that there is some ugliness to its design that has lasted even to the latest version due to Murex's compatibility promise. However, the latest version of Murex does provide an internally versioned runtime, which means scripts can now pin to a specific version of Murex and not worry about gradual changes over time (even if "gradual over time" in this context literally means "years of compatibility" even before the versioned runtime.
This means that Murex and Elvish might feel like very different shells despite being conceptually quite similar.
I'm a little reluctant to give specific areas where the two shells diverge because both are under active development and thus moving targets. So what might be true today might not be true tomorrow. However, I will say the syntax for each does vary significantly despite being superficially similar.
As for job control, this was part of Murex's early design because it's a feature I used heavily at the time. So the concept of background and foreground processes are weaved throughout all of the core runtime. Like with Elvish, Murex doesn't create new UNIX processes for builtins. And with commands that are forked processes, Murex doesn't hand over complete ownership of the TTY to them so that Murex can still catch the signals. The reason for the latter is because Murex can then add additional hooks to job control, such as returning a list of open files any stopped processes have opened, and how far through reading those files it is. So Murex has needed to re-implement some of the job control logic that would normally be handled by the POSIX kernel. This does result in a lot of additional code, and thus places for things to go wrong. On balance, I think I made the right tradeoff for Murex. However if I were to write an entirely new shell from the ground up, I'd probably not do it this way again.