Confirmed:
This issue has been identified as being caused by redstone clocks usually within the 12x12 chunk area, causing a 1 chunk wide FPS drop area between the always-loaded and sometimes-loaded chunks. This behavior has also been described outside the always-loaded chunks.

Not all clocks will cause this issue, and it is currently unknown why some clocks are affected and others are not.

Redstone Hoppper Clock: Tested and Confirmed
Redstone Comparator Clock: Tested and Confirmed
Minecart Clock: Untested

Unconfirmed:
This may be caused by additional redstone devices, and may not be restricted to redstone clocks. Additional reports have been submitted describing the same behavior related to item frames now that they are redstone-enabled, and have been related to this ticket.

Temporary Resolution:
Disabling certain redstone clocks within the 12x12 always-loaded chunk will remove the lag. Note that not all redstone clocks will cause this issue, you must find the specific clock causing the problem and disable it.

Server Recommendation:
Do not build redstone clocks within this area until the issue is resolved. If clocks are required, after activating, verify that this issue does not appear. If it should appear try moving your clock.