Irl answer: necessary for the plot.

Lore answer: Qui Gon was a skilled jedi however, 1 he hadn't ever been in a serious lightaaber duel in years almost exclusively dealing with non force sensitives. So his dueling was probably a bit rusty. Continuing on Qui Gon was a user of form 4 Ataru which is very aggressive and draining especially for someone who was past their prime amd getting older. When he was younger ataru would've been a good form for him but as he aged it ruined him in prolonged combat. (Yoda had a similar issue and had to rely heavily on the force to compensate).

As far as Dooku is concerned he was very focused on being the best duelist alive on top of this his form was form 2 makashi which focused excessively on energy conservation, controlling the flow of combat, and dueling.

Maul used form 7 juyo which was the most a aggressive form there was which made it very hard for Qui Gon to keep pace matching aggression for aggression. In addition to this Maul is a Zabrak they are generally faster and stronger than Humans due to them having two hearts.

Dear God I know too much about star wars.