toejam

Fishing won't be an option either place. Both parks get a big spring break crowd and have all their campsites fill up. Try to find out when the schools will be out and pick a week off the peak if possible. March is as good as the weather gets down there, but can be really cold at night. The wind blows like crazy sometimes.

Guadalupe doesn't have a lot of campsites and the backpacking sites require you to haul a ton of water on your back thousands of feet up the mountain. It's great if you like big climbs and big views. You have to see Carlsbad Cavern if you go.

Big Bend has more to offer, especially if you have a high clearance vehicle to get on the back roads. For backpacking, the trails from the Chisos basin are great and you can pick a spot not too far from the car. The Pinnacles sites are not too arduous with a pack on, you can easily get to Emory Peak from there. You may find water above Boot Spring, but you can't rely on it. Hiking up Juniper Canyon is quieter, but you have to drive a real rough road to get there. Juniper Spring is not a reliable source of water.

Big Bend Ranch State Park doesn't get quite the crowd and is worth checking into. It also has the backpacking route with the most reliable water supply in the area - the Rancherias Loop.

For backpacking with fishing in March I'd recommend the Gila Wilderness in New Mexico.