You need to do both sides as newer exhaust systems are "tuned".
Tuned exhaust means the exhaust system is setup to lower pressure at exhaust valves at a specific RPM.
With lower pressure the piston/crank doesn't lose as much power pushing exhaust out, so more power is available for the back wheels.
3rd party headers are tuned for low RPM power, factory exhaust is tuned for mid-RPM power.
You can also get racing headers that are tuned for high-RPM power
None "add power" they just change the specific RPM where the lowest pressure occurs at the exhaust valves.
The closer the engine is to that specific RPM the more available power it will have.
So you want both exhaust manifolds to be tuned the same.
The above is where the Myth of Back Pressure comes from.
People not aware of tuned exhausts would put larger pipes/headers on the engine, then go for a test drive.
"Hey, I lost power, WTF!!!"
"this engine must need Back Pressure"
No 4-stroke engine would run better with Back Pressure(2-stroke yes, lol)
What they did with the larger pipes at the head was to remove any possibility to generate lower pressure, so they lost the power that added.
The lower pressure is generated with velocity, smaller pipe means more velocity, when that smaller pipe dumps into a larger pipe(collector) there is a pressure drop.