I've been to Aegnia and Agistri many many many times, but only day-tripped to Aegnia, while staying on Agistri. That said, I disagree with the above poster, while Agistri is small it has many beaches. There is a shallow, sandy one right at Skala, which is now considered the main harbor. If you go left from there, there are shallow, pebbly beaches with beach clubs for quite a ways. If you go right, there's a short hill into the pine forest, from there you can have breakfast or lunch at Hotel Kekrefalia, where we used to stay, which grants you access to their "beach" platform, which IMO is the best experience - no sand, all relaxation, the most beautiful water. You can keep going up the hill to Skrili beach, which you descend briefly down a steep stone staircase (no handholds). I adore this beach, especially in the morning, but it's narrow and gets crowded by 11am in busy season. Two weeks ago I swam there from another hotel that doesn't offer beach access to people who aren't staying there, because at my age/stability it's easier to go up the steps than go down! Then you can continue further into the beautiful pine forest for amazing views and perhaps the most famous beach on the island, but it's a serious, very difficult scramble to get down to it. Even my hardcore hiker friends won't do it - i've only visited by boat, which you can rent as well.
The most beautiful swimming area is probably on the other side of the island, which is only 10 minutes by taxi or about 30 by bus, Aponisos, which does have a small fee but is absolutely stunning. There is a fish taverna that may rate highly although I find if you don't arrive by yacht, they don't much care about you.
The real main town, Milos, is small and hilly but has a beautiful church, but yes, but tourist standards, Agistri is pretty much there for beaching and relaxation.
Aegnia has a lot more going on, but the beaches aren't as nice. The old town is charming, has some lovely little fish tavernas, and really cool ruins you need to take a bus or taxi to get to. We did once and walked down to the village on the other side, but I wouldn't recommend that. Very impressive ruins, though!
I prefer to relax on Agistri and visit Aegnia as a half-day or day trip, but this is when I was living in Europe and Agistri was my beach vacation. That may not be a fit for everyone, but it's a little slice of paradise for me and everyone I've taken there has returned.
Also the previous poster is wrong, Agistri is served by the same large car ferries that go to Aegina. In high season, there's so many ferries these days, it's crazy. We did take a hydrfoil back, because it fit into our timing of catching a flight, but we always take the slow boat over and enjoy the ride and views on the outside deck when we can.\
Edit: To answer your car versus no car, that's a no-brainer, Agistri doesn't have many cars, people either rent e-bikes, scooters, or take taxis or the one bus (which just goes to Aponsisos) to get around. I've never rented any kind of vehicle in my time there although I was tempted to rent e-bikes.
Aegnia is more difficult without a car. We wanted to take a bus to the ruins up the hill, but despite waiting it didn't appear to be running, so we took a taxi. We asked him to come back in 2 hours to get us, but he didn't and we didn't have good cell reception at the time so we literally couldn't get a taxi up there which is why we scrambled down a rocky gulch and along a road with tour buses with no walkway (kinda scary!) to get to the nearest town, where we had the restaurant call us a cab so we could get back to port. Aegnia anywhere outside Aegnia town is best explored by vehicle IMO.
