Here are some differences between paper and film that will affect the image resolution acutance, resolution, and resolving power.
Paper: The emulsion normally used for paper is relatively insensitive silver chloride in a colloidal suspension, orthochromatic (blue sensitive), thickly applied to a fibre base with a baryta layer for brightness and a starch binder to hold the emulsion to the base. The ability of the image to enter the emulsion and re-expose from the base by reflection reduces the acuity of the image. The image tends to "bloom" and the point-spread-function increases more than doubling. This reduces the effective resolution. There might be some loss due to the paper base itself; but, I suspect minimal.
Film: The emulsion normally used for film is more sensitive larger crystals of silver iodide in colloidal suspension, panchromatic (red sensitive), thinly coated on a dimensionally stable flexible plastic (PET) base,
a protective transparent over-coat, a "binder" to hold the emulsion to the base. In addition, an anti-reflection coating is applied to the back of the base to prevent halation (double exposing the film emulsion due to retro-reflection of the source.)
It sounds like an intriguing experiment comparing the performance of the two.