My personal Jean Baptiste horn has mechanical linkage. At school, I use a Holton horn, which has string linkage. From my own personal experience, the mechanical linkage clicks and seems to stick a lot more than the string. Is it it just that my horn is "special", or are there more advantages to string than to mechanical?

Mechanical linkages must be well oiled (use thicker oil than for the rotors). If not they wear and will become noisy and need more serious attention ... The linkage is unlikely to stick its more likely to be the valve - most horn players leave dismantling and cleaning a rotory valve to qualified technicians because reassembling them is a little tricky!