Both of you are wrong
here is why
When with 1 fan being faster than the other, the faster fan will be doing more work relatively, the slower fan will be doing less work, with a lesser load on the fan because the faster fan will be pushing air into it
thanks to air resistance and the fact that there is not equilibrium in pressure, the slower fan will still have work to do in terms of helping air flow
No, having two different fans will not cause the premature death of the other fan.... What will end up hamper is one fan will hamper the other... In a sense, if you're adding in a faster fan, you will benefit. If you add in a slower fan YOU STILL BENEFIT. Why? Because its adding more static pressure drive.
The only real downside or negave effect is you lower your efficiency.
tl;dr - from an engineer, no there is no problem with different speed fans.