We do monitor server tick rates on LIVE using the same data I show in this chart. For the vast majority of servers in we see a steady 128 tick rate. We do have a problem where on round transition the server takes a long time to setup the initial frame and spawn everyone in. That's usually when you'll see low server FPS show up in the top right.
You can actually see server tick rate in your game if you go to Video -> Stats -> Server Tick rate. You can see a graph of server frametime in realtime. It's generally a boring straight line. There are specific regions and specific data centers where they ran hot for periods of time and start to dip but we're constantly adding hardware as it's available and the player base grows.
The more common "server problems" tend to stem from networking outages on the route from players to our servers and complications that cause dropped packets or significant increases in network latency. The network graphs also exist in the settings menu.
In terms of the feel difference you're seeing I can't be sure. My guess would be potentially high ping or packet loss but it's hard to say without seeing it. We're still working to improve the capabilities of Riot Direct and have added more data centers post-launch to help address outlier areas of poor ping. Hopefully any issues you're seeing will be address by this combination of efforts. We're always striving to get better.