Dooku and Grievous share some similarities. They both have damage reduction against melee attackers, with Dooku having a better-than-average dodge as well as two red cards that reduce his opponent's damage by one each. Each has three pips for moving and an instant-damage ability (Force Lightning and Unrelenting Assault). However, they play very differently because of their command cards: Dooku is more oriented around positional command card use, while Grievous has excellent aggressive options.
Health/Speed/Cost
When you compare raw numbers between these commanders, they're pretty close. However, when you look at the number of units a commander can be deployed with for a given cost, Dooku loses out to Grievous—four units compared to five at Elite skill level. Even if we assume both commanders are played optimally, that means that by simply having one more unit available in the same group, Grievous has an additional unit worth of firepower and crowd control. In addition to his fifth unit being stronger than Dooku's last, Grievous is faster and has a better health-to-cost ratio, so he will tend to get in more attacks before he dies or moves on.
Moving/Attacking
Dooku's extra unit gives him more flexibility in terms of moving around the board compared to Grievous, but this is where I've found Dooku tends to fall short. He lacks both Relentless and Charge, so he typically won't be engaging with enemy units as soon as they appear on the board. However, even if he could move up and engage with them right away, his lack of either ability often means that it becomes a coin flip as to whether or not he can kill them. Grievous, by contrast, has four red cards: Unrelenting Assault and Lightsaber Sweep for attacking enemies and Deadly Advance and Force Crush for moving into better positions. Grievous's move-and-attack cards are all double pips (except Deadly Advance), but that means that Grievous is at least guaranteed to do some damage when he uses them.
Defense/Disruption
Dooku's red defensive cards aren't horrible: you can mitigate up to thirty total points of damage, which is above average among commanders even without considering the positional flexibility. However, Dooku's extra unit does not help him defensively as much as you think since it doesn't change his number of units deployed.
