If you were trying to design a game like DayZ, WarZ, Rust, or H1Z1 from scratch, which engine would you use?
I understand that it's suggested I put this in "for beginners" but I'm not looking for beginner advice. I'd like to know what the pros would use.
It's not the most useful question -- what the pro's use is only the right choice for them because of their situation. Do you have a team of a dozen senior engineers who you're paying $100k a year, and a budget of $10M to spend on your game? If not, then the right choice for you will be different to the choices made by "the pros".
Personally, I'd probably build one from scratch specific to these requirements
...But I've spent 8 years working as an engine programmer, so I've got a lot of reasons to make that choice. If your team didn't have an experienced engine programmer, it would be a much more crazy choice to make.
If your team all have 5 years experience with Unity, then that would be a sane engine to choose. They're probably able to bend Unity to their will enough to pull off a DayZ.
If you've got experience with Unreal, that would be a good choice.
If you're an experienced Arma modder, then you could copy what DayZ did and start out as an Arma Mod!
A pro team would evaluate all their options and weigh up the pros/cons specific to their situation. One of the biggest weights in this is how much experience their team has with each of the engines. If engine B is slightly more popular in this genre but the team has previously shipped 5 titles using engine A, they're very likely to just continue using engine A and to perform any customization/extension required to make this next game.