1. Which was better at their job as warlord?
None of them was particularly good, but Mihawk was better than Doffy, no doubt about it. Doffy was working closely with one of the WG's strongest enemies (Kaido) and his main goal was to bring the world to a complete chaos, so he was undoubtedly more harmful to the WG. Doffy didn't even care about WG's direct orders, as seen in Marineford when he was dealing with Moria.
2. Which was more influential?
Now DoFlamingo easily takes the nod. He was the "Underworld King" (the most influential broker), while Mihawk preferred a reserved lifestyle in his castle... they had two completely different mindsets.
3. Whose defeat and arrest would be more impactful to the world?
Well, Mihawk wasn't defeated yet, but I think that DoFlamingo's defeat is more impactful due to his influence in the underworld. Mihawk's defeat would bring more "glory" to his nemesis though, as Mihawk's WSS title requires more strength.
4. Which was more free?
Mihawk certainly. Doffy was tied to Kaido and couldn't possibly step back. Mihawk had his tie with the WG, but severing it would only result on him going back to the seas, as it already happened after the end of the Shichibukai.
5. Which dresses better?
I particularly prefer Mihawk's clothes, but Doffy had his style.