Short answer. Yes — both are named grounds. Under Rule 93, Section 4 of the Rules of Court, any interested person may file a written opposition contesting the petition on the ground of the competency of the alleged incompetent or the unsuitability of the proposed guardian, and may ask that the petition be dismissed.
What the law says
Any interested person may, by filing a written opposition, contest the petition on the ground of majority of the alleged minor, competency of the alleged incompetent, or the unsuitability of the person for whom letters are prayed
Rule 93, Section 4 — Opposition to petition. Read the full provision →
What the law says
may pray that the petition be dismissed, or that letters of guardianship issue to himself, or to any suitable person named in the opposition
Rule 93, Section 4 — Opposition to petition. Read the full provision →
The grounds the rule recognises
Rule 93, Section 4 puts the two objections in the question squarely on the menu. An opposition may contest the petition on the ground of the competency of the alleged incompetent — that the person the petition describes as unable to manage themselves or their property is in fact capable, and needs no guardian at all — or on the ground of the unsuitability of the person for whom letters are prayed — that whatever the ward's condition, this particular petitioner should not be the one holding the trust. The two grounds attack different things: one denies that guardianship is needed, the other denies that this guardian should get it. An opposition can, and often should, raise both.
Who may oppose, and what they may ask for
Standing is broad: any interested person may contest, which in practice reaches the alleged incompetent themselves, family members, and others with a real stake in the person or the property to be placed under guardianship. The relief is broader than a simple no. The oppositor may pray that the petition be dismissed, or that letters of guardianship issue to himself, or to any suitable person named in the opposition. So a family that agrees their elderly parent needs help, but distrusts the relative who filed, does not have to pretend the parent is fully well — they can concede the need and contest the choice, offering the court a better guardian by name.
This rule is for adult wards, not minors
One boundary to keep in view: since 1 May 2003, guardianship of minors has been governed by A.M. No. 03-02-05-SC, the Rule on Guardianship of Minors, which amended Rules 92 to 97 of the Rules of Court in that respect. Guardianship of incompetents who are not minors continues to be governed by the Rules of Court — so Rule 93, Section 4 is the opposition rule where the alleged ward is an adult said to be incompetent. That is why the section's reference to majority of the alleged minor as a ground now does its work under the 2003 Rule's framework; for adult wards, the live grounds are competency and the proposed guardian's unsuitability.
Making the opposition count
The opposition must be written and filed in the guardianship case — the rule's phrase is by filing a written opposition — so the time to act is before the court hears the petition and appoints anyone. On competency, evidence beats assertion: medical evaluations, the person's own handling of their affairs, testimony from people who deal with them. On unsuitability, particulars again — conflicts of interest over the very property to be managed, financial irresponsibility, estrangement, or conduct showing the petitioner seeks control rather than care. And if you name an alternative guardian, choose someone genuinely suitable and willing, because the court will weigh your candidate as closely as the petitioner.