To marinate the catfish, mix salt, pepper, chili powder, cumin, brown sugar and paprika in a small bowl. Spread evenly over both sides of catfish fillets, place on a dish and cover with plastic wrap. Refrigerate at least 4 hours or preferably overnight.
About 1 hour before serving, prepare charcoal for grilling, and let burn until coals are hot.
To prepare the corn relish, brush corn lightly with some of the olive oil, and lay on the grill rack over the hot coals. Grill, turning often, until golden on all sides. Cool. Cut kernels from cobs with a sharp knife into a large bowl. (There should be about 1 ⅓ cups.)
Heat remaining olive oil in a small skillet over medium-low heat. Add garlic and cook, stirring often, about 10 minutes or until very soft and fragrant. Cool and add to bowl of corn kernels.
Cut tomatoes in half, and gently squeeze out seeds and discard. Dice the tomatoes. (There should be about 1 ⅓ cups.) Add tomatoes and green pepper to corn mixture. Mix in lemon juice, salt and pepper. Taste salad, and adjust seasonings if desired.
To grill the catfish, brush the marinated fillets with olive oil, and lay on the grill over the hottest part of the fire. After about 30 seconds, turn fillets 90 degrees, and grill on the same side for 30 seconds longer. Move the fillets to a cooler part of the fire, and cook 2 minutes longer on that side. Turn over, and cook 3 to 4 minutes on the other side, or until fish flakes easily when tested with a fork. Just before the fillets are done, brush with barbecue sauce.
Place the grilled catfish on serving plates, and spoon corn relish over them. Garnish with fresh basil leaves.