Which type of control unit used in modern processor?
x86 are famous for using microcode, because there are a few complex operations, such as call gates or how the x87 calculates sines or exponentials, which cannot be reasonably constructed with a simple finite state machine. x86 also have very extensive patching resources, which allows to fix some bugs on released silicon, and which is probably handled through microcode (Some hints are probably in the patents from Intel and AMD). 

Small ARM CPUs don't need and don't use microcode. The "R" and "M" classes.

High end ARMs such as Apple's... Who knows ? Besides the visible instruction set, there are also many hidden stuff, for example for debugging, self-testing the hardware and for power management, which may be based on microprograms.

The general trend nowadays, is that, even in x86, the instructions that need performance are decoded directly which is faster and more power efficient that fetching microcode memory.