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Generally, a higher tick-rate server will yield a smoother, more accurate interaction between players, but it is important to consider other factors here. If we compare a tick rate of 64 (CSGO matchmaking), with a tick rate of 20 (alleged tick rate of Overwatch Beta servers), the largest delay due to the difference in tick rate that you could possibly perceive is 35ms. The average would be 17.5ms. For most people this isn't perceivable, but experienced gamers who have played on servers of different tick rates, can usually tell the difference between a 10 or 20 tick server and a 64 tick one.
Keep in mind that a higher tickrate server will not change how lag compensation behaves, so you will still experience times where you ran around the corner and died. 64 Tick servers will not fix that.
If you are concerned about the performance of the game, there are a few things you should rule out first, that can make a significant difference:
Your internet connection. The lower the latency the better. This is why its important to play on the servers on which you have the lowest latency. Also any congestion on your home internet connection can cause delays. Lag compensation helps with the "what you are shooting" part, but if you have poor latency, you are much more likely to experience the "I ran behind a corner and still got shot" scenario or the "I shot first and still died" scenario.
If your client has a poor frame-rate (anything lower than or close to your monitor refresh rate), this will increase the delay perceived, often by more than the difference tick rate makes.
Tweak your interpolation if the game allows it. Most games will have a default interpolation period that is at least 2x the duration between ticks, the idea being that if a single packet is lost, a player movement will not stutter on the client screen. If your internet connection is good, and you have zero packet loss, you can safely set the interpolation period roughly equal to the tick duration, but if a packet is delayed, you will see a stutter. In CSGO for example, this will make a larger difference than moving from a 20 tick server to a 64 tick server. If you set this too low, it WILL cause choppiness.
If the game allows you to increase the client update rate, you should do it if you want optimal performance. It comes at the cost of more CPU and bandwidth usage, however on the client side this usually doesn't matter unless your home internet connection has very low bandwidth available.
If you have a monitor refresh rate of 60Hz, then you probably can't tell the difference between a tick rate of 64 and 128, because your monitor can't even display the difference attributable to the tick rate.
One final note:
We don't actually know what the tickrate of the servers is, I saw the thread with the wireshark capture, and it shows the client receiving packets every 50ms. This would indicate 20 tick, but this is only true if the client update rate = the server tick rate. Often the client update rate is a parameter that is set locally in the client that will be sent to the server when the client connects. The server then sends updates at that frequency. The server may actually be running at a higher tick rate, but if the client update rate is set to 20, then the server will only send an update every 50ms.
So before you crucify the developers over 20 tick servers, figure out what the tick rate actually is, and whether the client update rate can be changed in a config
TL;DR; Very few people actually understand "netcode", but are happy to complain about getting killed when they are behind a wall.
Edit: Reddit Gold! Thanks mysterious benefactors!
Edit: A good write up on the difference between 64 tick and 128 tick servers: http://mukunda.com/128tick.html