If you compare 2 identical mics/systems - one wired and the other wireless:-
The wired system is best when you want minimum interference AND you are trying to replicate and maintain (as much as possible) the actual signal coming in (your voice), with an average budget.

Wireless systems tend to not do well with lower frequencies unless you get into the $2000.00+ systems like the Shure UR4D with KSM9 mics or SABINE's SW72*** series where special circuitry is incorporated to 'make up' for this loss.

You can really experience this IF you go to the store and try them out side by side... then you will know what is 'missing' when you decide to go wireless.

Another brand that does a good job to rectify this in their wireless systems (for way less $$) is Sennheiser. Sure Shure do make great wired mics, but when going wireless, it may help to explore others ... especially since it's not all mic manufacturers who design and/or build their wireless systems - on which the quality of these great mics depends on ... eventually.