USB mouse, like any other USB device, shares it's bandwidth with other USB devices. And if you have many USB devices working at the same time, you can get higher latency (longer response time) with your USB mouse. Though, there are different polling rates for gaming USB mice, ranging from 125 Hz to 1000 Hz that minimize the latency (e.g 1000 Hz = 1ms response time) but if the system that deals with USB packets hangs, you'll get higher latency either way.
PS/2 mouse, in the other hand, sends dedicated signals to the PC which interrupts anything CPU is currently doing and forces CPU to deal with the PS/2 input. In that sense, PS/2 mouse and KB are far better since you won't get any latency with them.
Another bonus for PS/2 mouse is that it doesn't require any dedicated software to work and works just fine with any PC that has PS/2 port. Most gaming USB mice have their own dedicated software to control them and at times, that software can cause issues.
Though, USB mouse also has it's advantages over PS/2 mouse. Most notable one is the DPI changing one the fly which many gaming mice support.
For example, my Corsair Sabre RGB has 6x different DPI presets that i can change with the dedicated buttons on my mouse. While i'm usually using 3000 DPI, depending on a game, i have changed it to 6000 DPI and 1500 DPI for better gameplay. 2nd thing about my mouse's DPI is that i have another dedicated button that changes my DPI to 400 and back, making the sniper shots ideal.
In that regard, PS/2 mouse falls behind considerably since you're stuck with the DPI it has. Unless you increase/decrease the cursor speed from Win and/or game settings.
Another bonus for USB mice is that many of them also have (RGB) LEDs for eyecandy while PS/2 mice usually lacks any LEDs. Though, LEDs are aesthetical and doesn't affect the mouse's performance.
I've used both, the PS/2 and USB KB and mouse for gaming for years and when it comes to my personal opinion, USB KB and mouse are better than their PS/2 counterparts. Though, i still keep my PS/2 KB and mouse around as backups, just in case i need them for troubleshooting the PC issues where PC fails to load USB drivers and none of the USB devices work.