I've been through this a couple of times but I think it is worth a quick summary.
I'm not going through definitions here. Let's just say that a hexcrawl means exploring a territory that is divided by hexes, with no clear paths, and a pointcrawl means exploring a territory through preexisting paths and points of interest.
This is a typical hexcrawl map (source). Notice the lack of clear paths. We might have to count hexes to know the fastest way from k2 to k6, and we don't know if there is a road; this indicates that important details are missing form the map.
This is a typical pointcrawl map (source). You cannot make your own path; to get from Gettysburg to Grafton you must pass through Harper's Ferry.
You can have both at once (source):
Notice that some regions (upper right) have no clear paths. it's up to the travelers to choose their own way. For other places, there is usually no reason to avoid the roads; but we still have to calculate how long each road takes.
When to use each?
Well, I'm convinced that pointcrawls are more useful and hexcrawls are only good for an specific (but very popular) type of campaign: one in which the PCs go exploring the unknown wilderness beyond civilization.
Pointcrawls, on the other hand, are useful if you're dealing with roads, cities, caravans, or even when going though the wilderness with a guide; if the guide knows a place, it knows a good path to this place. A dungeon, with rooms and corridors, resembles a pointcrawl.
One thing about pointcrawls is that you should focus on paths, instead of only points of interest. How does the Old Road look like, and what kind of creatures use it, how long does it take to travel it? Etc.
This kind of information is also important for any hexcrawl that uses roads or trails; why count hexes every time you go through a road instead of having these numbers beforehand?
And this forces you to think about the journey itself (or "expeditions"), which is good. You can estimate the duration of your travels. You can keep "STRICT TIME LIMITS" in a meaningful way.
As I've said before, Curse of Strahd should be a pointcrawl. Tomb of Annihilation would be a mix of both; the PCs rely on guides, so the paths should be previously known until they go out on their own. Descent into Avernus could be either; the abstract territory of Avernus shifts and changes.
The problem with pointcrawls, of course, is that you usually have fewer tools when you go "off the road" or get lost. However, this is not hard to calculate, and if you use the same way more than once you can add a new path to your map. The paths that already exist are used often even before you arrive; making new ones could be part of the adventure.
What about urban adventures? Well, most of the times they are neither. We are not dealing with wilderness, obviously, but streets are not exactly roads either; the path you take from point A to point B is often unimportant in most of our city dealings (barring ambushes, etc.). Maybe city adventures must be construed as a web of events or NPCs instead of places, but that's the subject for another post. If the city is in complete chaos or ruin, an hexcrawl might be a better fit, provided "zones" of the city are more important than specific streets.
http://hillcantons.blogspot.com/2012/01/crawling-without-hexes-pointcrawl.html - start here. this is the post that started it all AFAICT.