Is it better to add a data file or better to increase the existing files (MAXSIZE)
Is there anything special to keep in mind with fail over clusters?


No


  Is there any reason why to prefere one of the options?


Yes, especially depending on your IO subsystem.  SQL Server uses two algorithms when deciding which file to use for allocating new extent. Round robin and proportional fill. My recommendation will be to use your first option.

I could use ALTER DATABASE with MODIFY FILE to increase the size of the existing files (~1TB each at the moment).


  Round robin means that the SE will try to allocate from each file in a
  filegroup in succession. For instance, for a database with two files
  in the primary filegroup (with file IDs 1 and 3, as 2 is always the
  log file), the SE will try to allocate from file 1 then file 3 then
  file 1 then file 3, and so on.
  
  The twist in this mechanism is that the SE also has to consider how
  much free space is in each of the files in the filegroup, and allocate
  more extents from the file(s) with more free space. In other words,
  the SE will allocate proportionally more frequently from files in a
  filegroup with more free space. This twist is called proportional
  fill.
  
  Proportional fill works by assigning a number to each file in the
  filegroup, called a ‘skip target’. You can think of this as an inverse
  weighting, where the higher the value is above 1, the more times that
  file will be skipped when going round the round robin loop. During the
  round robin, the skip target for a file is examined, and if it’s equal
  to 1, an allocation takes place. If the skip target is higher than 1,
  it’s decremented by 1 (to a minimum value of 1), no allocation takes
  place, and consideration moves to the next file in the filegroup.


Paul Randal explains this in details with example,
Investigating the proportional fill algorithm.