Regarding fewer parks in the suburbs, I'm not sure this is true, at least not true for all cities. Here's how far (by foot) public greenspaces are from my parents' suburban house according to google maps.
4min: park with tennis courts, playground and baseball field
6min: park with several gardens and access to Lake Ontario. It's a good place to meet people and is often used for wedding pictures.
6min: schoolyard with soccer field and basketball courts
10min: park with public outdoor pool, playground, baseball field and wooded ravine
11min: schoolyard with soccer field
11min: park with playground, grass field and wooded ravine
13min: small park with public lake access
15min: a couple little parks, just wooded/swampy ravines
16min: wooded ravine
18min: tennis courts
19min: schoolyards with track, football, soccer and baseball fields, basketball, wooded area and playground
20min: schoolyards with soccer, baseball fields, basketball, wooded area playground
In the end, at least around here, the 20th century suburbs tended to avoid burying creeks like in the 19th century, and kept ravines around them. School yards also got bigger, with larger sports fields. I wouldn't say this is a suburbs vs cities thing though, as much as a product of the times.
Mid/late 20th century development in the cities also had a lot of greenspace with apartments/rowhouses in the park, and then when that didn't work out so well, with better defined public greenspaces. In Toronto, this shift started in the 70s and 80s, and the redevelopment of industrial and waterfront areas near downtown now includes a fair bit of parks, and also some courtyards. In addition to courtyards, you also have something similar to SoCal's bungalow courts, except with townhouses, as well as a lot of private outdoor terraces on condos.
Nowadays, there is a push (at least around here), to protect a ton of different kinds of natural areas, not just ravines but also waterfronts, woodlots and wetlands. My parents' suburb is planning to develop the Northern part of the municipality to hold 50,000 people and 30,000 jobs, and the park area would be almost 3 times Central Park:
www.mshplan.ca/
NorthOakvilleEastSP.pdf
There are several different kinds of parks, and they serve different purposes. One type I'll call "play areas", sports fields/courts, playgrounds and dog parks where you, your kids or your pets can go play or be active, but also end up being social places since you play with others, and if you're a parent or pet owner, it's a good platform for socializing with other parents or pet owners. Then you have plazas which exist mostly for socializing, and squares and gardens which are for both socializing and relaxing. Finally you have natural areas like ravines and woods that are more for escaping the city, and people. Some of these benefit from getting a fair bit of use (the social ones), some benefit from getting little use (natural areas), some are in between. Some require lots of space, some do well with little space. Some also can have a mix of purposes, like a playground with an area next to it for parents to relax or socialize. Where I find suburbs often fall short is when it comes to places for people without pets or children to hang out, from teenagers to seniors.