You should read the guidelines carefully. Not every field/journal/conference will see things the same way. In particular it may depend heavily on whether you are asked for a reason for exclusion. Note that previous co-authors are easily spotted in bibliometric systems (including the journal's in-house system if you habitually publish there); competitors are harder to find.
According to AIP's ethics guidelines.
Privileged information or ideas obtained through peer review must be
kept confidential and not used for competitive gain. Reviewers must
disclose conflicts of interest resulting from direct competitive,
collaborative, or other relationships with any of the authors, and
avoid cases in which such conflicts preclude an objective evaluation.
Thus the onus is on the reviewers. However (from memory, if I'm wrong I'm thinking of another publisher) when you're asked for reviewers to avoid, you're also asked to provide a reason. By stating that you are competing with another group you can help the editor make a judgement call bearing in mind that in the editors' responsibilities section:
Situations that may lead to real or perceived conflicts of interest should be avoided.
The editor may think "perfect, someone who can review this really critically" and choose to ignore your suggestion (that's all it usually is) but then they have to be able to stand by this decision. It could affect how they choose the other reviewer(s). But you need to be specific and polite -- not "Prof X has it in for me" but "Prof X's group are working on very similar material and we feel it would be a conflict of interest if they were to see this work ahead of publication".