What is the difference between these two types of hose in terms of performance? I notice that transmission oil cooler hose is slightly thicker and heavier than power steering return hose.

Is it OK to use transmission oil cooler hose on a power steering return?

Is it OK to use power steering return hose on a transmission cooler?

Thermoid's catalog gives the following specs for transmission cooler hose:

Application Transmission Oil Cooler
Style N/A
Grade N/A
Specification SAE J1532
Branding Thermoid Transmission Oil Cooler (Size)
Made In USA (Date)
Cover Color Black
Construction
Tube Nitrile
Reinforcement Polyester
Cover Nitrile/PVC
Temperature Resistance -30 Degrees F to +257 Degrees F

The specifications for power steering return hose:

Application Power Steering Return
Style N/A
Grade N/A
Specification SAE J189
Branding Size I.D. SAE J189 Made In USA
Cover Color Black
Construction
Tube Nitrile
Reinforcement Polyester
Cover Polychloroprene
Temperature Resistance 250 Degrees F

As far as I can tell the biggest difference between these two hoses is the cover, polychloroprene vs. nitrile/PVC.