Generally speaking, the participial clause, starting with -ing or -ed, is more characteristic of written English, as it allows us to say the same thing as a relative clause, starting with who ...
Note that if the subject is the same in both clauses, a participial construction may be used, particularly in written English. Compare the following: 'She completed her first novel while working ...
A participial phrase consists of a participle plus modifier(s), object(s), and/or complement(s)’. An earlier column discussed gerunds which, basically, are verbs with the ‘ing’ ending.