If by "plate armour", you mean armour with substantial metal plates, they used that:

• https://qph.fs.quoracdn.net/main-qimg-7dce85f5280981dd751565c49bd277c9.webp

• https://qph.fs.quoracdn.net/main-qimg-32caeeca7adeb586c3c8095ceb1e9aa5

• https://i.pinimg.com/736x/2f/d8/2a/2fd82a809a7fb5c916759a79a39654a5.jpg

• http://www.antiques.com/vendor_item_images/ori_1910_485565441_1156574_es850.4.jpg

Also many armours with small plates, including late mail-and-plate armours with large areas covered by the (small) plates

• https://i.pinimg.com/originals/72/55/f1/7255f18d153b72805d16b8444df7ce98.jpg

and earlier lamellar armours.

These are not as protective in some ways as good European plate armours (less face protection on helmets, mail at joints on shoulders rather than overlapping plates, etc.) but some offer fewer gaps than European plate (with mail over gaps - some of which would have sometimes been covered by mail under the plate (either a separate mail shirt, or just pieces to cover the gaps attached to the arming garment), but sometimes would have been gaps with no metal armour). Plate-and-mail armours with good coverage would be as protective against most weapons as a typical full suit of plate armour (and more so than a typical munition plate armour).

The biggest difference in protectiveness might be against pistols - late 16th century and early 17th century European 3/4 plate armours offered reasonable protection against pistol shot, a sensible choice given the widespread use of pistols as cavalry weapons at the time. Ottoman and Persian cavalry retained the bow as their ranged weapon, and had less motivation to seek pistol-proof armour (a pistol ball hitting the mail portion of a plate-and-mail armour could be quite effective).

Given Ottoman expansion into Europe at the time when plate armour reached its peak in Europe, the Ottomans don't appear to have suffered from their non-adoption of European style armour. Not everything went the way that the Ottomans wanted, such as their failure at Belgrade in 1456. Ottoman art shows a small fraction of the defenders in plate armour, which the Ottomans lack:

• https://commons.wikimedia.org/wiki/File:Siege_of_Belgrade_(N%C3%A1ndorfeh%C3%A9rv%C3%A1r)_1456.jpg

but their loss was more due to the strength of the defences and the breaking of their naval blockade which allowed the city to be reinforced and resupplied.