This isn't exact as I can't find a way to only select matches where both players took the new ball, so the below stats are a bit rough but are generally only a few matches off so I think give a generally good reflection. Fwiw I have taken late 90s as starting in 1996 and early 00s up until 2004.
Stats for bowlers in position 1 or 2 in matches from 1996 until Ambrose retired
CA Walsh - 38 matches, 168 wickets @ 22.04, 9 fivefors, 1 tenfor
CEL Ambrose - 37 matches, 136 wickets @ 20.55, 8 fivefors
Stats for bowlers in position 1 or 2 in matches where Gillespie bowled in position 1 or 2 from 1996 until 2004
GD McGrath - 52 matches, 235 wickets @ 20.67, 13 fivefors, 1 tenfor
JN Gillespie - 53 matches, 197 wickets @ 25.26, 5 fivefors
Stats for bowlers in position 1 or 2 from 1996 until Donald retired
AA Donald - 49 matches, 226 wickets @ 20.46, 15 5wi, 1 10wm
SM Pollock - 44 matches, 165 wickets @ 22.12, 7 5wi, 0 10wm
Stats for bowlers in position 1 or 2 from 1996 until Wasim Akram retired not including Shoaib Akhtar
Wasim Akram - 27 matches, 98 wickets @ 23.39, 5 5wi, 2 10wm
Waqar Younis - 27 matches, 96 wickets @ 27.52, 1 5wi, 0 10wm
Edit: I should read the thread first
, just seen Ginge has been statsguruing this also. Could've saved myself 45 mins or so of my life.