Manned missions would still have constraints. In some cases, they would be far greater (e.g. due to the necessity of keeping the astronauts alive). Where there are fewer constraints, it would be intertwined with the cost of sending people to Mars. They may be able to travel faster, but a lot of that is going to be because of a larger energy budget. It is doubtful they could travel further, since there are still going to be limits on how far they could travel (humans need infrastructure). That said, perhaps they could cover a larger area (within a smaller radius) than robots. Risk is also a limiting factor, and it is a far bigger one with people. Humans may be more flexible, but you aren't going to have those romantic scenes of people scaling down steep slopes or spelunking in caves. It could be done, but the chances of something going wrong will inhibit it.

While on the topic of human flexibility, it is important to understand that it will be limited due to the resources available. What we saw on Apollo 13 wasn't the product of people trying to expand beyond the mission objectives with what is on hand, it was a last ditch effort to save the Apollo crew. They could afford to do unintended things with the equipment on hand since the only other option was to admit defeat then let people die. Even the very much fictional The Martian was based upon that premise. Treating it as a thought experiment: the primary response was to terminate the mission and evacuate. The part about the lone survivor on Mars was about ditching every mission objective in the name of survival. It would be very difficult to even create a fictional narrative of a human team going beyond the abilities of a similarly appointed robotic mission without abandoning reality altogether.