When I play a FPS with my wireless mouse I feel that the game reacts more slowly than my movements. Is a wireless mouse less reactive than a classic mouse? Is there a loss of performance with wireless mouse? What is the latency of a classic mouse or wireless mouse? How can I test that?
Wireless mice have several disadvantages for gaming, latency being one of them. They also have a nasty habit of dying just as you're about to get the game-winning kill. It may or may not be the biggest/only bottleneck to your gaming performance, but it's certainly true that more gaming mice exist that are wired than wireless.
As far as testing it goes, you could take a look at this article, which contains testing suggestions and tuning opportunities to measure the latency of you wireless mouse versus a wired one.
It really depends on which mouse, I have the Logitech G Pro that has 4.8 ms input lag and there are no spikes at all, it will light red when the battery is low and it last for 60 hours without RGB lights or 45 with full brightness. An office wireless mouse or just a low-end one, or something that uses Bluetooth may be bad for gaming. If you want to go wireless I suggest you try a solution with a dongle and a custom wireless technology, Logitech uses "lightspeed" for example. Wired mice will always be faster, but between 1ms and 4-5ms is really impossible to feel the difference.