Code density is the biggest one. If I want to add two numbers with a stack design I have an add opcode. If I have 128 instructions that's 6 bits of opcode. I only need one because the add opcode will pop the two numbers off the top of the stack and push the result back on. If I want to add two numbers with a register design I need to specify which registers which means if I have 16 registers I need 4 bits per operand minimum which means 12 bits just for the two sources and destinations. If I'm trying to write for an embedded system you can't get higher code densities than using a stack machine.

The instructions can also execute faster because I don't have to do things like decode registers and look them up in the register rename table but modern CPUs pipeline this shit so well you never have to worry about instruction latencies.

For register based machines one big advantage is that it's way easier for compilers to optimize for register based systems. If I have a common value that I'm using constantly if I was using a stack based arch I'd have to keep pushing that value to the stack. With a register machine I just slap the value in a register and use it as an operand as many times as I need.