There's a long page on the Tardis wikia which details many of the changes, and shows how sometimes it is merely a case of the makers discovering something they like:
Deep Breath saw the debut of a new title sequence originally designed
by Billy Hanshaw, after executive producer Steven Moffat discovered a
popular video of the graphic artist's conceptual Doctor Who title
sequence on YouTube. Moffat, delighted with how new and innovative
Hanshaw's ideas were, got in touch with him to create a professional
version of his sequence for the actual series.
Note that this title sequence was often slightly changed:
Starting with The Magician's Apprentice, the clock gears, the gas and
the first clock face tunnel have a purple hue.
This sequence received many one-off modifications during its usage. In
Death in Heaven, the Doctor's appearance was replaced with that of
Clara Oswald (Jenna Coleman) and her credit placed before his to
reflect her ruse to the Cybermen that she was the Doctor. In Heaven
Sent, Capaldi's name is held on the screen longer - as he is the only
actor credited in the title sequence.
When this title sequence was used in Christmas episodes, a wintry feel
was given to the title sequence. In Last Christmas, the first
unwinding clock is icy/frosty and the TARDIS is covered in snow.
Snowflakes appear in the second Time Vortex and the special guest
credit for Nick Frost as Santa Claus is delayed until the sequence is
And one episode had a completely different title sequence:
The title sequence introduced in Deep Breath was temporarily ditched
for a silent title card, which was used to to fit with the "found
footage" theme of the episode. This title card features the names of
the characters and locations from Sleep No More alongside randomly
picked numbers. The words 'Doctor Who' can be seen spelled vertically
through the names of other characters. The title of the episode is not
seen in this title card, and instead appears during the closing
credits, including the writer, Mark Gatiss and director, Justin