The streetcars I'm most familiar with are directly connected to the power grid through overhead lines, and are on rails. Cars would need batteries as private cars won't have a pantograph, or fuel. In either case, there are more things that can break in a fleet of smaller vehicles, so maintenance is higher. Cars also use rubber wheels on pavement, rather than steel wheels on rails, so have higher rolling friction.
Streetcars can also handle a high density of passengers. This is important for rush hour, when the load is high. A streetcar has about 3x the capacity of a similarly sized bus, which is in turn much higher than passenger vehicles. In turn, as the article points out, streetcars are best when they have dedicated right-of-way, which allows a higher throughput and predictable latency compared to cars, which are more subject to gridlock. Also, the improved capacity feeds back on itself when people build high-density (eg, 5 story buildings instead of single family houses) along streetcar corridors.
The more recent streetcars are also better designed for a wide variety of users. For example, some of the ones I know have a platform which is only slightly above the curb level. This makes it easier for a parent pushing a stroller, or someone with difficulties walking, or on a wheelchair, to enter the streetcar unassisted. The same is not true of most cars.
Finally, there are some environmental difference. A personal vehicle has the advantage of not sharing space with strangers. It has the disadvantage that you and your 9 friends can't all travel together. And a streetcar is usually a much smoother ride; a friend get nauseous after 10 minutes as a passenger in cars and buses, but not in streetcars.
So while what your friend says is true, there are other factors which make it less compelling.
But everyone still uses the streetcar system because you can get from point A to B, no matter if B is half a mile or 5 miles away, for one fee of $2.10 vs ride-sharing or taxis which accumulate charges over time and distance.
Taxi?!
The self-driving aspect makes it a bit similar to a streetcar in that it should not deviate from the road, as does the on demand aspect: in it's glory days in city centers they were everywhere close to you at regular times so you'd never had to wait long before before one was available.
Anyway, whether one finds it similar to streetcars or not, the most compelling about such system is that it would, together with a mentility change away from 'car is king', probably be able to get rid of a lot of traffic jams and more importantly all the problems they pose. Because it basically is a form of decentralized (must be good, right :P) public transport which is lacking now in most countries and cities: something which can get you from A to B at any time of the day or night without requiring walking/cycling to intermediate points where you then have to wait for your bus/train/.. to arrive.