Here is the problem I see.
Signal strength = the connection between the closest cell site and the device
Network speed = a combination of 2 things:
1- the actual rate data can be transferred to/from the device
2- bandwidth - or the amount of data that can be handled by the network before bogging down
Best way to visualize this is the freeway concept. If you have a 3 lane freeway that has a speed limit of 100 mph and a 6 lane freeway that has a speed limit of 70 mph, the speed limit of the freeways is a factor if there are only a few cars on it. Now put rush hour traffic with the same amount of cars on each freeway. The people going through the rush hour traffic are going to have "faster" speeds on the 6 lane fwy (even with a slower speed limit) at a certain number of cars because the capacity of the 3 way is much less and bog it down. Take away the cars and yes, the 3 lane 100 mph freeway will blow the 6 lane away. Fill them with equal capacities maxing out the 3 lane and those on the six lane will have a breeze of a drive.
Cell providers advertise their network "speeds" (speed limits) based on their rate of data transfer, not their bandwidth capacity (how many lanes). This is why in some areas, AT&T has a "faster" network (hspa), but a verizon device could still be faster on 3G when comparing similar downloads side by side. This is why there is so much confusion about whose network is faster. The providers are playing a ruthless and cheap advertising game that hurts one person, the consumer.
4G, as advertised by the carriers means little as it does not describe what it used to, a generation of technology. None of the upcoming "4G" networks will be true 4G. It is unfortunate that the carriers have chosen to so badly confuse the consumer with a combination of omissions and misinformation.