There are many factors at play here.
Ping, this is the time a packet takes to be send from your pc, to the server, and send back to your pc again. in miliseconds.
Most important for the game to feel smooth is having both the player and the server with a very solid connection, no wifi (very very important!) because the problem is not ping.. the problem is fluctuation in ping.
Lets say you have an average value of 20, it sounds awesome, but if your internet is unstable and it fluctuates +- 10 milliseconds... that is shit. and can create prediction and timing problems for the player and the server. so for sure don't play on wifi, and try to see if you have ping fluctiations by doing a ping to the server your playing on, and see if any ping spikes..
Regulary restarting your router can fix most of these delays, also some switches in your house might be shit, or the router is just bad and you should replace it with a high performance model.
On top of that high fps is important, though with a limit, in my experience don't let your client have a higher fps than 200. Because it can create timing inaccuracies.
The game is mostly CPU limited nowadays, so you can even crank the graphics settings up full, makes no difference anyway, on my laptop i even have 500 fps if I don't limit it
But by all means see how your system reacts to the settings.
For the server, it is running on about 111-124 fps depending on intervals at the moment. it is a hardcoded fps limit. and hopefully the server is very fast and not loaded heavily, a full server with a lot of players or bots will run on a lower FPS, because the CPU is loaded.. and thus all things will be affected and register less good. which you probably experience in big events.
Important in this case is having a extremely fast server CPU, single threaded that is, think about like a core i7 at overclocked 5 ghz, that will register great!.
How warband combat works, on click your client sends a message to server, which sends it on to the other players, there is no server side prediction or ping compensation, lower ping player is always on advantage, he can see what the other players are doing faster, and he can faster get a reaction to it to the server, for instance getting a block in just in time, whilst a player with higher ping won't be in time.
The physics engine of warband is running on 0.025 interval, meaning 40 times per second it is doing all physics calculations, for hit detection and much more, in that same interval it is also sending packages, data gets collected and send off in those intervals.
If you have any questions please ask them.
If you have any suggestions to make the combat better then say so.