It's worth remembering that only the RAC and AA have their own mechanics. Their vans are akin to mobile workshops and well stocked with loads of common spare parts, such as bulbs, fan belts and batteries. So they're particularly well equipped to fix a breakdown at the roadside.
Other services though, like Green Flag or the firms mentioned above, simply contact a local garage who work under contract to them. They tend to turn up in a pickup truck with just some basic tools with them. That means that they're probably less likely to fix a problem at the roadside and more likely to tow your vehicle to a garage (or convey you home if you've got a relevant level of cover).