No, you cannot file Form 990 or 990-EZ instead of IRS Form 990-PF as form 990-PF is an information return that needs to be filed specifically by Private foundations.
As private foundations operate slightly differently than other tax-exempt organizations, provided your organization qualifies as a Private Foundation, then you'll need to file Form 990-PF with the IRS and make sure to provide all the required information for a complete return.
However, any information return that needs to be filed by your organization will primarily depend upon your organization's gross receipts.