Where to start, first Palo Duro activities include horseback riding, hiking, nature study, bird watching, mountain biking, and scenic drives. There is also the Official Play of the State of Texas which returns to the Park. It will run Tuesday through Sunday beginning Friday, June 5.
Also the museum (not in the park) is worth the time. And the BIG TEX steakhouse in Amarillo is good eatin!
You can not really compare the two parks.
Both have much different vista's, one being a canyon in the desert, the other being in the hills along a stream. Garner offers hiking, nature study, picnicking, canoeing, fishing, swimming in the Frio River, seasonal miniature golf, paddle boat and kayak rentals (mid-March through Labor Day weekend), and bike riding (surfaced).
Again worth the trip, Palo Duro is much bigger but no water to speak of. Palo Duro is a lot less crowded but it is in the dessert not along the Frio. Both can be fun.
Take DH to both !