They made the correct choice.
The Cowboys took Ware with the 11th pick of the first round and Merriman went to the San Diego Chargers with the 12th pick.
Merriman had 39.5 sacks, including a league-high 17 in his second season, in his first three years. He had six in his final five years as injuries ruined his career.
Ware finished his career with 138.5 sacks, eighth all-time in NFL history. The seven players ahead of him are each in the Hall of Fame, so are the two players behind him.
"Everybody in the building knew he was going to be special," Minnesota Vikings head coach and former Dallas Cowboys defensive coordintor said on ESPN Radio KESN-FM 103.3.
"I can still remember some of the plays we watched on tape when he was at Troy. They were playing LSU and they were backed up about the 10-yard-line and they ran a draw or something. He came up the field, turned the corner, accelerated back and made the tackle on the back. You'd see plays all day long like that with him.
Coach Bill Parcells actually wanted to take defensive end Marcus Spears with the 11th pick to anchor his defensive line because the Cowboys were transitioning from the 4-3 defense to the 3-4.
But owner Jerry Jones and the scouting department overruled Parcells because they figured the only way to get both players was to select Ware, the pass-rusher, first.
"I thnk everybody felt really confident about DeMarcus," said Mike Zimmer, the defensive coordinator at the time. "We felt we'd get two good players, which we did."
Ware and Spears had forged a friendship playing at the Senior Bowl, competing at the NFL scouting combine and rooming together in the Cowboys' rookie minicamps and training camp.
"It was an opportunity to really get to know each other and share the journey together," Spears told ESPN Radio KESN-103.3 FM. "We grew up together going through the growing pains of the NFL. He's not just a teammate, he's a friend."
While Ware's position was designed for him to sack the quarterback and make game-changing plays, Spears' role was to stop the run and free the linebackers to make plays in the Cowboys' defense.
Ware had eight sacks as a rookie. He had at least 10 during each of the next seven seasons, including a career-high 20 in 2008. He made nine Pro Bowls and was name First-team All-Pro four times.
"He had unbelievable talent, he was very intelligent and he was a hard worker," Zimmer said. "You knew right away that he was different than everybody else."
Spears started 89 of 119 games with the Cowboys. Spears finished his career with 10 sacks.
Envy could've easily ruined their relationship if they hadn't respected each other.
"All of the tags were given to me. 'He's a bust. He's a wasted draft pick. We should've drafted Aaron Rodgers. We should've drafted whoever,' but you know for me it was about the respect and words from coaches and guys inside that locker room.
"We were both first-round players. I came from a bigger school and D-Ware was making all kinds of crazy plays and going to Pro Bowls and I wasn't. It was human nature for people to compare us.
"But the football minds and people around the game understood our jobs totally different, so it was never hard to manage our relationship. D-Ware was one of the strong voices when I was young, dumb and stupid and reading and listening to what what people were saying. He said, 'You're doing a hell of a job, keep doing what you're doing."
That's among the reasons Zimmer calls him a better person than a player.