As stated, modern emissions has almost no effect on power or economy. I like them, I don't like sniffing the results of a dirty tailpipe anymore.
Now in the dark days of the mid to late 70's, it was a different story. You could take an engine, pull the emissions stuff, but in a normal cam and carb and it would run a LOT better. The original catalitic converters were pellet type, basicly forcing the exhaust to flow through a can of gravel sized media. Those sucked for flow. Hence the "pull it off and it will run better". But every modern (mid 80's and up) cat is a honeycomb substrate. You can see straight through it (although only in a bunch of straight lines). The flow is nearly as good as a stright pipe.
EGR can do some neat tricks. Done right (and that generally means computer controlled) it adds dead exhaust gasses to the combustion chamber. This causes incrased cylinder pressures. More cylinder pressure gets you more bang per drop of gas. I have seen published ½ MPG increase by adding EGR from reputable sources (non-profit, non-marketing publications). The dead gases also absorb combustion heat that the elevated pressures create, so the chamber actually runs a touch cooler (less NOx emissions). So higher pressures, burn the fuel better, get more work for the burn, and reduce NOx emissions. It is closed at idle and full power so those do not get affected. Great thing to run.
Evaporative (charcoal canister). No effect on how it runs at all. In theory a touch better MPG as it is now burning the gasoline vapors instead of just letting them go. Again a system that only works at cruise. Best part is the garage isn't as stinky of gasoline vapors.
Really there isn't a downside to modern emissions stuff.
