These days both fibre and twisted pair are supporting 1000BASE-T and 10GBASE-T, but when do you choose one over the other? The obvious one is maximum cable length, but what are other factors which might come to mind when making this choice. 
There are a fairly large number of factors to consider and it is also important to accept that not all fiber is the same just like not all twisted pair is the same.  Here are a few things that occur to me.  Of course these may vary depending on environment.

Fiber:  Much longer max distances, depending on specification and throughput.  No electromagnetic interference. Note however that fiber comes in a large number of grades and planning for the future may be somewhat more complex.

Copper: Shorter max distances per link.  Susceptible to electromagnetic interference.  Fewer number of grades/variations (but still mind these!) meaning fewer accidents when the rollout team grabs the wrong spool (see below for a funny story).  Supports power over ethernet.

Funny story:  A particular county in a Western state runs a fiber network that began as a control system for their hydroelectric dams.  As time went on they found they didn't need nearly as much fiber as was laid for this and so they separated out many of the strands and used it to build a county-wide network linking homes and businesses to ISP's and telco's.  Of course single mode fiber was used for longer transmissions and multi-mode for short runs.

So when they were running the longer runs to connect towns and cities with this new network, the team that ran the fiber grabbed the wrong spool, and ran multi-mode fiber on all these long distance links.  The team was quite unhappy when they found out they would have to re-run all the fiber again!  Moral of the story:  be very careful about ensuring that everyone knows which grades of fiber go where....
