Which to use of ps ef or ps -ef?

man ps says:

This version of ps accepts several kinds of options:

1   UNIX options, which may be grouped and must be preceded by a
    dash.
2   BSD options, which may be grouped and must not be used with a
    dash.
3   GNU long options, which are preceded by two dashes.

So, ef uses the BSD e and f options, and -ef uses the Unix -e and -f options. These are different (sections SIMPLE PROCESS SELECTION, OUTPUT FORMAT CONTROL and OUTPUT MODIFIERS respectively):

   -e     Select all processes.  Identical to -A.
   -f     Do full-format listing. This option can be combined with many
          other UNIX-style options to add additional columns.  It also
          causes the command arguments to be printed.  When used with
          -L, the NLWP (number of threads) and LWP (thread ID) columns
          will be added.  See the c option, the format keyword args, and
          the format keyword comm.

   e      Show the environment after the command.

   f      ASCII art process hierarchy (forest).

Clearly, you're not selecting all processes using the ef options, but are using the default listing of processes, plus some additional formatting:

By default, ps selects all processes with the same effective user ID
(euid=EUID) as the current user and associated with the same terminal
as the invoker.  It displays the process ID (pid=PID), the terminal
associated with the process (tname=TTY), the cumulated CPU time in
[DD-]hh:mm:ss format (time=TIME), and the executable name (ucmd=CMD).
Output is unsorted by default.

The use of BSD-style options will add process state (stat=STAT) to
the default display and show the command args (args=COMMAND) instead
of the executable name.  You can override this with the PS_FORMAT
environment variable. The use of BSD-style options will also change
the process selection to include processes on other terminals (TTYs)
that are owned by you; alternately, this may be described as setting
the selection to be the set of all processes filtered to exclude
processes owned by other users or not on a terminal.

Which should you use? What do you want to do with the output?

Also, see the EXAMPLES section (which does list -ef rather prominently, and doesn't use the BSD e option at all):

EXAMPLES

   To see every process on the system using standard syntax:
      ps -e
      ps -ef
      ps -eF
      ps -ely

   To see every process on the system using BSD syntax:
      ps ax
      ps axu

   To print a process tree:
      ps -ejH
      ps axjf

See man ps (the one on your system, on-line can have different explanations).

This version of ps accepts several kinds of options:

   1   UNIX options, which may be grouped and must be preceded by a dash.
   2   BSD options, which may be grouped and must not be used with a dash.
   3   GNU long options, which are preceded by two dashes.

So the 1st method (ps ef) is BSD style and the manual page goes on with

The use of BSD-style options will add process state (stat=STAT) to the default display and show the command args (args=COMMAND) instead of the executable name. You can override this with the PS_FORMAT environment variable. The use of BSD-style options will also change the process selection to include processes on other terminals (TTYs) that are owned by you; alternately, this may be described as setting the selection to be the set of all processes filtered to exclude processes owned by other users or not on a terminal. These effects are not considered when options are described as being "identical" below, so -M will be considered identical to Z and so on.

So both are valid commands but they are not showing the same information.