The best shooter games like Virtua Cop are Time Crisis, House of the Dead: Remake and Virtua Cop 2. Below are 9, each with the reason it is here — and, at the end, what filtering to shooter costs you.
Filtering to shooter means you want the guns to be the answer. It is the right filter when what you liked was the feedback — the sound, the recoil, the way enemies react.
What you get: Moment-to-moment feel, and the shortest distance between picking a game up and enjoying it.
What made Virtua Cop worth playing in the first place is covered on the full list. This page is the shooter part of that answer, and only the shooter part.
The other arcade pillar, and the pedal changes the whole genre.
The spectacle end, rebuilt for modern hardware.
More of the same with branching routes and better weapons.
If you have VR, this is where the genre went.
A modern rail shooter designed for a controller.
Nintendo's target shooting, deeper than it looks.
Where pointing at a screen started.
Aiming and moving as separate jobs, by Treasure.
The direct descendant of the hunting-gallery idea.
Variety. Shooters commit hard to one loop, and the ones that try to be something else usually do the something else badly.
The full list is on games like Virtua Cop — 9 picks, no genre filter.
Time Crisis. The other arcade pillar, and the pedal changes the whole genre.
No. Virtua Cop released on the Sega Saturn, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
How the guns sound and how enemies react to being hit. A shooter with mediocre levels and superb weapon feedback is more fun than the reverse, every time.
Each pick says. Several of the best shooters ever made are single-player campaigns, and a few of the co-op ones are genuinely worse with bots.
By hand. Each pick was written for the full Virtua Cop list first, on what the game actually does, and this page is the part of that list that is shooter — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the shooter guide for where to start in the genre generally.