The 870 QVO uses slower QLC flash memory. QLC has a very low native write speed, though under most typical usage scenarios that will be hidden by a much faster SLC cache, which temporarily holds written data until it can be stored in its permanent location. On the 1TB 870 QVO, that cache size can be up to 42GB. If you write more than that to the drive within a short period of time, sequential write performance drops from around 500 MB/s, down to just 80 MB/s, until the drive gets a chance to clear the cache and recover.
https://www.anandtech.com/show/15887/the-samsung-870-qvo-1tb-4tb-ssd-review-qlc-refreshed/2
The MX500 doesn't use this cheaper QLC flash memory, so it's able to maintain its full sequential write speed near 500 GB/s without having performance drop during very large writes. As for when you might encounter such a scenario on a gaming system, it's possible that such a slowdown could occur when installing or updating a large game that extracts all its files at once, or when copying over a game directory from another drive.
As far as load time performance in games goes, all of these drives should perform relatively similar, as they are all limited by the SATA interface, which limits maximum sequential throughput to around 500 MB/s. Judging by the benchmarks listed in that review though, it looks like the 870 performs worse as the drive becomes more full, while the MX500 performs about the same either way. At a similar price, I would absolutely take the MX500 over the 870 QVO. The MX500 is more comparable to Samsung's EVO drives, while the QVO drives are somewhat more budget-focused offerings.
Edit: If this sounds similar to Popotim's post, it's because I wrote it a couple hours ago, but had to head out for a bit before getting a chance to read it over before posting. : P