To an extent, it is a matter of personal preference or style. Cicero used participles sparingly and preferred whole sentences, Caesar used them more frequently for his trademark compact style and peppered his writing with ablative absolutes. Both were and are considered paragons of good Latin.
But are there any fixed rules? Yes, there are certain guidelines, but they are somewhat vague and not consistently adhered to even in antiquity, let alone in later periods.
However, according to Johann Philipp Krebs it is considered good classical style to follow these rules:
- A relative clause should be used when the idea is to identify or specify the thing/person we are talking about.
- A relative clause should also be used when expressing an inherent, permanent property of the thing or person.
- A relative clause should be used when the preceding noun is accompanied by a numeral.
So if it's not clear which speaker we are talking about, and we want to identify him by reminding our readers of his petition for peace, we say:
Illum oratorem, qui finem bellorum petivit, non adiuvistis.
Slightly exaggerated English translation: “That speaker who was asking for an end to the wars – you didn't help him.”
But if we want to narrate the story of how someone asked for peace and got no help, we can say:
Illum oratorem petentem finem bellorum non adiuvistis.
Again, a somewhat exaggerated translation: "When that speaker was asking for an end to the wars, you didn't help him." But note, it is my understanding that nobody would object to a relative clause here either.
Likewise, we should say:
Flumen est Arar, quod in Rhodanum influit.
(There's a river called Arar that flows into the Rhodanum; Krebs' example from Caesar for an inherent permanent property.)
Duos oratores, qui finem bellorum petiverunt, non adiuvistis.
(Example for a numeral.)