If Bullseye had started out as a Punisher villian instead of a Daredevil one would he have been killed sooner. Everytime these two fought there was always an excuse for Punisher to not kill Bullseye. Like in the Punisher vs Bullseye series and the Punisher Countdown sorry I don't have the scans to show you guys but if anyone does mined posting.
The Punisher vs Bullseye
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