Vaughn was placed on the disabled list early on during the 2003 season due to the deterioration of one of his knees. It turned out he would never play again. Vaughn played in 29 games, batted 79 times, hitting .190, 3, 15 for the 2003 Mets. Delgado was put on the DL during the 2009 season, after playing in 26 games, batting 94 times for a .298, 4, 23 clip. And neither ever played again, though Delgado made a comeback for the Boston Red Sox in 2010, hitting 3-13 for the Pawtucket Red Sox before hanging it up for good. Vaughn's injury was more frustrating, as it seemed like he never tried to come back. However, the damaged to his knee, where it was bone-on-bone, resulted him remaining on the 60 day DL until his contract ran out after the 2004 season. Some even got upset at Vaughn after he filed for free agency after the 2004 season. It was just a formality, officially ending his tenure with the Mets.
In my opinion, both players were very good when healthy, something that Delgado maintained better than Vaughn. Delgado was the more prolific run producer, driving in 100+ runs 9 times, while Vaughn had 6 such seasons. Vaughn had 2 40 HR seasons to Delgado's 3.
I think one of the best ways to compare the players one against another is to compare their best individual seasons. While both had more than one season that could be used, I chose Delgado's 2000 season with Toronto vs Vaughn's 1998 season with Boston. Delgado, for the 2000 Blue Jays, hit .344, 41, 137, playing in 162 games, 569 official ABs with 115 RS, 196 hits, 57 2Bs, 1 3B and 123 walks, 104 Ks. His OBP was .470, SLG .664 for a 1.134 OPS to go with his 378 total bases. Vaughn in 1996 hit .326, 44, 143, playing in 161 games, 635 official ABs with 118 RS, 207 hits, 29 2Bs, 1 3B and 95 BB, 154 Ks. Vaughn's OBP was .420, SLG .583 for a 1.003 OPS with 370 total bases. Based on that, I think Delgado had the more dominant season. However, I find it amazing that Delgado had only 10 more total bases in 2000 than Vaughn did in 1996.
The best way to compare is to give an average of what each player would do over the course of a 162 game season. Thanks to baseballreference.com, it is determined that Delgado averages .280 (his career average), 38, 120 over a 162 game season in addition to his 88 walks and 139 Ks. Vaughn hit .293 for his career, with an average of 35 HR and 114 RBI over the course of a 162 game season, with 78 BBs and 153 Ks. Comparing their career OBP, SLG and OPS, you'd see that they both finished with the same career OBP at .383, but Delgado, known to hit more 2Bs, had the slightly higher SLG of .546, to Vaughn's .523 for a .929 to .906 OPS advantage.
Delgado and Vaughn are not often compared to each other even though they played the majority of their careers for division rivals. Vaughn started playing every day in 1993, while Delgado became a regular for Toronto in 1996. They technically only were division rivals for three seasons, 1996-1998, before Vaughn left as a free agent to California.