We've done both over the years.
We shared a car until shortly after DD was born. We moved to where we live now partly because it has good public transport locally and to the city centre (suburbs).
We had 2 cars for the next 8 or so years - I used to drive to city centre daily and DD came home with me, DH used to drive or cycle and DD would go in with him in mornings (she's great at signaling when cycling herself now due to all that training on the back of his bike!!
) until DD went into primary, then I needed to collect her from afterschool club by car as it was too far to walk late in the evenings. We also managed to use public transport for periods in there rather than car commuting.
DH was away 50% of the time for a period (2 weeks away, 2 weeks at home) so we dropped to 1 car again. We were able to juggle when he was home, and we agreed up front that we'd use public transport mostly but if there was an urgent or late night out type need or clash of diaries, occasional taxis were part of the budget too. And we also knew there are 2 decent car hire places very locally if we had significant clashes for a weekend or similar. These costs were a lot less than running a second car, and not so much hassle that we couldn't do it.
Then DFIL died, 2.5 hours away, and DH spent weeks down there while he was ill, and weeks and many many weekends more supporting DMIL after he died. Meanwhile, I still had to work and DD still had school here. So we went back to 2 cars. He really needed one down there (public transport really didn't work long term as DPIL live rurally a bit away from the city down there) and I really needed one up here (DD activities scattered locally not all on public transport routes, needing to do grocery shopping as online wasn't great, etc).
It worked ok while we only had 1, but it did require a lot of communication and understanding and a fair amount of flexibility from both of us. But having gone to 1, we also were happy to spend on taxis, where others in the family wouldn't, and we are all happy to use public transport (even with work/activity gear). DH and DD cycle a fair amount (my bike is rusting away unloved) as well, for fun as well as to get places, and DH can commute on his (he can even walk to work half the time - but then he also has to get to the airport at 4am most weeks and gets home the following night at close to midnight - so definitely needs his own car for that!). And we will all walk locally to do errands or meet people.
But DD seems to need a lift to/from school more than ever in secondary (loads of books and loads of sports gear) and it is a good 45 minute walk away, late in the evening in the dark and cold of winter.
And we have got involved in both sailing and in scouting in the past few years, both of which involve significant amounts of gear being hauled around the place, and generally to places with no public transport (small harbours all over the country, and up boreens to go on hikes in the depths of the countryside!).
And I must admit that I have got much more used to the autonomy of having my own car since DH was working away (and didn't need the family car), and now that we got a 2nd one the 2nd time around, so it would be harder for me to give it up a 2nd time.