It's a rough estimate based on clock cycles. The Z80 instructions take between 4 and 23 cycles to execute, with an average of about 13 cycles. The 6502 instructions take between 2 and 7 cycles with an average of about 4, thus the difference of about 13 / 4 = 3 times more cycles. It doesn't take into account how much is being done by each instruction or memory timing, etc.
Another reason the 6502 is faster is it was designed to utilize the bus on every other clock cycle, leaving the other cycles for a co-processor such as a video chip to read memory without impacting the speed of the processor. The C64 (1 MHz w/2 MHz RAM) and BBC Micro (2 MHz w/4 MHz RAM) both used this feature. The Atari 800 didn't and lost from 10% to 47% of its processor cycles to the video chip.
The Z80 also has more addressing modes, which speed things up. It depends on what type of computing you are doing. For most games, the 6502 @ 1 MHz is faster than the Z80 @ 3 MHz, but at maths, the Z80 is faster.
Another reason the 6502 is faster is it was designed to utilize the bus on every other clock cycle, leaving the other cycles for a co-processor such as a video chip to read memory without impacting the speed of the processor. The C64 (1 MHz w/2 MHz RAM) and BBC Micro (2 MHz w/4 MHz RAM) both used this feature. The Atari 800 didn't and lost from 10% to 47% of its processor cycles to the video chip.
The Z80 also has more addressing modes, which speed things up. It depends on what type of computing you are doing. For most games, the 6502 @ 1 MHz is faster than the Z80 @ 3 MHz, but at maths, the Z80 is faster.