Wired is measurably better, and I will give you the numbers rather than an opinion. Whether it is worth a cable depends on which benefit you are buying.
On an Xbox Wireless Controller, across our testing, USB sits around 8 to 13ms, the Xbox Wireless Adapter sits around 12 to 18ms, and Bluetooth sits around 15 to 25ms. So wired versus the adapter is a gain of roughly 4 to 6ms, and wired versus Bluetooth is roughly 7 to 12ms. Those are real differences and they are consistent across sessions. They are also, for almost everyone, below the threshold of perception. Research on input latency perception generally puts the detectable difference for most people somewhere above 20ms for this kind of task, and a 5ms improvement is not something you will feel as a difference in responsiveness.
So if raw speed were the only consideration, I would tell you to stay wireless and stop thinking about it, which is what you said you wanted to hear if the difference was tiny.
But raw speed is not why I use a cable in competition, and here is the argument that I think actually applies to you. Wireless introduces variance and failure modes that wired does not have. The latency figure fluctuates with radio conditions, so your delay is not a fixed number but a range, and your timing adapts better to a stable delay than a variable one. More importantly, a wireless controller can drop out, and it will choose the worst possible moment to do it. A battery can die mid-match. Another device can crowd the band. None of those happen on a cable.
For ranked play where you are trying to remove excuses, that is the real reason to go wired: not that you will aim faster, but that nothing will surprise you. Run the test yourself on both connections for a minute each, and look at the spread rather than the average. If your wireless spread is tight and your battery habits are good, wireless is a defensible choice. If the spread is wide, that is your answer.
