The phone provider isn't specifically collecting location information, usually. They're collecting usage data about their phone masts, so they can upgrade bandwidth to heavily used ones, plan maintenance out of peak usage hours, and other technical reasons. This includes details about devices which are connecting to a given mast at a given time, since it's useful to determine things like handover.
Google will try to collect more accurate positioning data. They can use GPS to pinpoint phones to within a few metres or so reliably. This can be sent to Google to enable various features like preparing offline maps of commonly visited locations, being able to notify you about travel delays on commonly used routes, and being able to tell you about local services when you search on terms like "restaurant" or "police station". In order to get that data to Google, there needs to be some kind of internet connection active - WiFi or mobile data.
If a criminal is using a phone, and they are sensible, they'll make sure that they've disabled the precise positioning data upload (they can still use Google Maps, if they've got an offline map - that just requires the phone itself to know where it is, and be able to find that on a pre-downloaded map file). That means that the precise positioning data isn't available. However, the cell level data is still around - that doesn't require any data connection, just a standard mobile signal. If the criminal wants to use a mobile during the crime, they can't cover that up. And it doesn't even have to be active use - mobile phones try to connect to nearby masts on a regular basis, so they can receive calls. They'll sometimes try and see if another mast has a better signal, too.
There isn't any particular reason why a phone provider couldn't collect more precise location data - they could pre-load phones they supply with monitoring software, for example. However, it would be a bit of a PR nightmare to deal with. There also isn't any particular reason why criminal investigations can't ask Google for the information, but it tends to be harder to tie a specific device to a location - the data tends to be collected on an account level - and may well involve international requests to get the data, whilst phone provider data will usually be available with a local warrant from a judge in the source country.