In layman's language, what is the difference/improvement in
performance when using a Fibre Optic Link instead of Microwave to
transmit Video (TV) pictures and Data (Internet?

Picture quality should be the same for either microwave or optic. Data
errors should likely be less in optic link than micro wave but very
rare for either system.
 There are differences in reliability, inital cost, maintanance,
valnerability to vandals,and wire tapping that are peculuar to the
length and location of the link. More detail may help get an answer.
Were you thinking of a particular contractor (supplier) for either or
both? Perhaps the link you desire is a few feet rather than a few
miles?  Neil

The only disadvantage about (not) using Microwaves is that Microwave
links require line of sight - that is, the transmitter and receiver
should have an unhindered path. However fiber optic cables, since they
are wired connections, can run anywhere.

Performance-wise, fiber optic cables have lesser error rates compared
to microwaves, because microwaves may get distorted or attenuated -
the chances of which are lower in sealed data cables.