Well, for one, the Soyuz can only carry a crew of 3, whereas Crew Dragon can potentially carry up to 7, and is designed specifically (for NASA's purposes) for carrying 4. This alone adds significant flexibility to the crew levels of the station. Since the end of the Shuttle era the ISS has been stuck at only 6 crew, precisely the number that can come up and return on 2 soyuz capsules. With the addition of Crew Dragon in the mix it'll be possible to support 7 crew members on the station with just 1 Dragon and 1 Soyuz capsule. The ISS requires a lot of maintenance and routine tasks, even adding one crew member would significantly increase the amount of science they're able to do on the station.
Also, increasing the diversity of crew transfer vehicles is very helpful. Right now there are 4 different varieties of cargo vehicles that visit the station (Progress, HTV, Cargo Dragon, and Cygnus). This diversity means that delays or periods of downtime with any one of the cargo delivery systems can be made up for via the others, as has happened in the past. The same resiliency has not existed for some time in regards to crew transfer vehicles. Given that there was a failure during an attempt to launch a Soyuz capsule last year which put a serious strain on the station (potentially putting it in jeopardy of being left uncrewed for some time) you can see that this is a serious issue.
Additionally, Crew Dragon is the first new crewed spacecraft to visit the station that was designed within the last decade, or, indeed that was designed this century. Soyuz is reliable but it has a great many constraints and shortcomings, many of which can't be alleviated without moving to a new design. It's refreshing to see that we as a species still have the capability to build new crewed vehicles with new capabilities and new designs rather than simply shuffling about as custodians of legacy vehicles designed and built by previous generations.
Even more excitingly, the Crew Dragon was launched by a vehicle which landed the first stage, and will have its first stage be reused on a future flight. The Soyuz rocket/capsule is a remarkably inexpensive way for crew to get to orbit, but those low costs are due mainly to sticking with an old design (all the R&D has long been amortized) and reliance on inexpensive Russian labor. Falcon 9 is already cost competitive with the Soyuz and has the potential to be even cheaper as Falcon 9 first stage reuse becomes more common. As reusable rockets become more common and familiar, and as their design improves with increasing use and follow-on generations (Blue Origin's New Glenn, SpaceX's BFR/Starship, etc.) costs will continue to fall and access to space will open up. Which will bring about a new space age where many more people visit orbit per year, space stations become much larger and more advanced, and our capabilities in spaceflight are in general much greater than they are today.
Also, increasing the diversity of crew transfer vehicles is very helpful. Right now there are 4 different varieties of cargo vehicles that visit the station (Progress, HTV, Cargo Dragon, and Cygnus). This diversity means that delays or periods of downtime with any one of the cargo delivery systems can be made up for via the others, as has happened in the past. The same resiliency has not existed for some time in regards to crew transfer vehicles. Given that there was a failure during an attempt to launch a Soyuz capsule last year which put a serious strain on the station (potentially putting it in jeopardy of being left uncrewed for some time) you can see that this is a serious issue.
Additionally, Crew Dragon is the first new crewed spacecraft to visit the station that was designed within the last decade, or, indeed that was designed this century. Soyuz is reliable but it has a great many constraints and shortcomings, many of which can't be alleviated without moving to a new design. It's refreshing to see that we as a species still have the capability to build new crewed vehicles with new capabilities and new designs rather than simply shuffling about as custodians of legacy vehicles designed and built by previous generations.
Even more excitingly, the Crew Dragon was launched by a vehicle which landed the first stage, and will have its first stage be reused on a future flight. The Soyuz rocket/capsule is a remarkably inexpensive way for crew to get to orbit, but those low costs are due mainly to sticking with an old design (all the R&D has long been amortized) and reliance on inexpensive Russian labor. Falcon 9 is already cost competitive with the Soyuz and has the potential to be even cheaper as Falcon 9 first stage reuse becomes more common. As reusable rockets become more common and familiar, and as their design improves with increasing use and follow-on generations (Blue Origin's New Glenn, SpaceX's BFR/Starship, etc.) costs will continue to fall and access to space will open up. Which will bring about a new space age where many more people visit orbit per year, space stations become much larger and more advanced, and our capabilities in spaceflight are in general much greater than they are today.