ScaryMary:
Thinner. You should put the same thickness of material down over those planks as the piece you removed. That looks to be about 3/8 inch thickness approximately. So you would use whatever thickness of material that that you took out because that would result in the floor over the planks being flush and level with the surrounding floor.
If someone told you that you need to nail down 3/4 inch plywood over those planks, they simply didn't understand the situation.
You should understand that it's those planks that provide all the strength to your floor. The "underlayment" that you removed (and now need to replace) doesn't provide any strength. It's just there to provide a smooth surface over which to install the final flooring material.
You don't need to know the rest:
Normally when the build a house, they have floor joists which are supported by concrete walls of the house's basement. Over top of the floor joists they will nail down 1X6 plank or 3/4 inch fir plywood, and that layer of planks or plywood is called the "SUBFLOOR". Then the 2X6 exterior walls and 2X4 interior walls of the house are built on top of the subfloor. If the subfloor consists of planks, as it does in your case, the planks will be nailed down at an angle to the joists because doing so results in a more rigid construction than nailing them perpendicular to the joists.
Then, they would normally nail down something called "UNDERLAYMENT" inside each "room" of the house to provide a smooth surface to install the flooring over. In your case, you have particle board underlayment.
One of the benefits of installing plywood underlayment over a plywood subfloor (for example) is that if you ever want to remove flooring that is glued down, like sheet vinyl or carpet, you can pry the underlayment up with the flooring still glued to it, and then put down new underlayment to install the new flooring over. That would save a great deal of work trying to remove the old flooring.