VPS speed varies significantly between providers and so do the CPU models they use to power their host machines. With more than 100 VPS tested over the past two years, our database includes the long list of CPU models used in all plans. In total, there are about 40 distinct CPU models being used from the Intel Atom to the Xeon Platinum.
This is the full list: VPS Plans by CPU Model
The first remarkable fact about that list is the complete monopoly Intel has over the VPS server CPU market. Until two years ago, there were still a few VPS providers using AMD chips in their hardware but they're now all gone, the lineup is 100% Intel and 90% Xeon.
The second interesting data point is that there are so many different Xeon models that two VPS providers rarely use the same ones. On the other hand, each provider tends to use the same CPU model in all of its plans. Take for example Amazon EC2/Lightsail who almost exclusively uses "Intel(R) Xeon(R) CPU E5-2676 v3" processors.

Linode obviously has a weakness for "Intel(R) Xeon(R) CPU E5-2680 v3" processors regardless of the plan while Ramnode prefers the "Intel(R) Xeon(R) CPU E3-124x" models. In terms of processing power per CPU core, the E3 is generally considered to be faster than the E5 and it's also often clocked higher. The advantage of the E5 lies in its ability to use more RAM and to pack more cores than the E3.
Few providers use the most recent Xeon Scalable also known as the Xeon Gold and Platinum processors. The only test we've run on one of those is the DigitalOcean - CPU Optimized 4GB and that was a "Xeon(R) Platinum 8168 CPU @ 2.70GHz".
Is there a correlation between the CPU model and how the VPS performs? Well, it depends what kind of performance you're focused on. At vpsbenchmarks.com, we are lucky to have detailed performance data coupled with the exact specs of all the VPS we test. This is the list of CPU models sorted by sysbench operations per second
If you're looking for the fastest web response times, don't spend too much time tracking the right CPU, the data shows the correlation is weak between CPU model and web performance. For example, consider the "Xeon(R) CPU E5-2680 v3 @ 2.50GHz" model, it was used in 6 separate Linode trials at vpsbenchmarks.com and it yielded web response times apparently randomly distributed between 60ms to 140ms. Naturally, the more expensive Linode VPS performed better than the cheaper ones on the same model, proof that disk IO and memory speed matter just as much as the CPU when it comes to serve a web page.
But there a strong correlation between the CPU model and the sysbench cpu performance. It's easy to see in this list that the processors that deliver the most ops/second are those that are clocked at a high frequency (3GHz or higher) or the most modern ones (the Platinum one used by DigitalOcean or the "Xeon E5-2687W v4" used by Upcloud.

There is also the case of Google Compute Engine that is hiding the exact CPU model they use ("Xeon(R) CPU @ 2.30GHz") and whose frequency is rather low but that manages to extract more than 350 ops/sec from their VPS.
VPS Providers rarely advertise the CPU models they use for good reasons: trying to guarantee all VMs for a particular plan run on the same type of hardware would soon become a logistical nightmare. But some providers offer CPU related options in their VPS plans: DigitalOcean promises "best in class Intel CPU" in its Optimized Droplets and Vpsdime lets you pick higher frequency cpus. It doesn't come cheap in either case but if the purpose of the VPS is to run compute intensive tasks, it might very well be worth it.