I would go as far to say that a relative clause is more a hallmark of golden age Latin, while participles gain in popularity in later writing. I'm mostly thinking of Cicero versus Seneca. A preference developed for a more terse, less diffuse, 'pointed' style of writing which would, as Cato points out, naturally favor succinct participles over additional clauses.
In regards to brevity, if I may add something I thought interesting, in an introduction to some letters of Seneca, there is a discussion of the stylistic features of silver age Latin. The editor compares expressions of the same intent:
Cicero:
Cupidis enim rerum talium (sc. uoluptatum) odiusum fortasse et molestum est carere, satiatis vero et expletis iucundius est carere quam frui.
vs. Seneca:
Hoc ipsum succedit in locum uoluptatum, nullis egere.
Cicero:
Quamquam quis est tam stultus, quamuis sit adulescens, cui sit exploratum se ad uesperum esse uicturum?
vs. Seneca:
(Mors) tam seni ante oculos debet esse quam iuueni: non enim citamur ex censu.
citamur ex censu: 'summoned on the principle of the levy', where the censors assigned to each of the two classes of citizens (iuniores and seniores) its own distinct function.