Difference in speed? Yes
Noticeable difference? Probably not.
The "polling rate" of the mouse measures how many times per second (in Hz) the mouse reports its relative position to "the computer". A higher rate means it reports more frequently. Most mice these days are around 250 Hz, older mice are usually 125 Hz. Is the human eye be able to register the difference between a rate of 125 "movements" per second vs 250 per second? Probably not.
Some gaming mice are (or at least advertise to be) 1000+ Hz per second. Keep in mind that the higher, the Hz, the more CPU "power" is required to register the signal from the mouse.
DPI or dots per inch, is how far your mouse moves across the screen with each movement of the mouse. These are usually options on the mouse (gaming mice typically have a button you can push to change the DPI and maybe the color so you know your current DPI). DPI is important if you have a high resolution monitor (4k) where pixels are so small that moving across 100 of them is a much shorter distance than a low resolution monitor. On lower resolution a high DPI can actually work against the user as one small movement of the mouse can send the cursor flying.
Keyboards have a few different measurements for speed, but the difference is so negligible that these speeds are rarely even reported in technical specifications. Like mice, they have a polling rate, but again, differences are almost always negligible and having a high polling rate keyboard will consume more CPU resources. Keyboards also have a matrix scanning time (1ms - 10ms typically), which is how long it takes for the keyboard to scan all the keys (hardware dependent). If a key is pressed, it "stores" the key in a temporary buffer. Then an algorithm (.5ms to 10ms) determines if the event was "real", and if so, releases it from the temporary buffer and "hands it off" to await being sent to "the computer" (when is determined by the polling rate).
Now, to actually answer your question, USB versions have a "minimum bus interval", which impacts the theoretical maximum polling rate a peripheral device can have. For example: USB 3.1 has a minimum bus interval of 125 μs, so the theoretical maximum polling rate is 8000Hz. Here's what I could find:
USB 1.1 and 2.0 - Low Speed
Max Polling Rate: 125 Hz
USB 2.0 - Full Speed
Max Polling Rate: 1000 Hz
USB 2.0 - High Speed, USB 3.0, and USB 3.1
Max Polling Rate: 8000 Hz
*Keep in mind, however, that there are other factors that can impact peripheral performance, such as your operating system, and device drivers.