Let me be clear about a couple of things. The BTU rating I am talking about is the maximum output of the primary or main burners, those burners under the cooking grate that you actually use for grilling. This is not the BTU output of the side burner, rotisserie burner, smoker burner, sear burner, etc. Some manufacturers and retailers try to fool you into thinking a grill is much more powerful than it is by lumping all these burners together. As for the square inch part, I am talking about the size of the main cooking grate. This does not include warming racks and other cooking surfaces above or outside the grill surface. Again, some manufacturers and retailers try to lump these measurements together to make you think you are getting a bigger grill than you actually are.
Power versus Efficiency: An inefficient grill, one that can't hold inside the heat that it generates, one with lightweight components, needs a higher BTU output so that it can grill a steak in the amount of time you expect. A good grill is heavy, its metal parts, particularly the cooking grates, heat up and hold that heat. A good grill has small vents to let a controlled amount of air flow through the grill, holding in heat so it heats up quickly to a high temperature.
The Infrared Exception: Infrared grills, of course, are different. While the burners of a standard gas grill heat the cooking chamber by convection, an infrared grill converts the heat of its burners to radiant energy. This makes infrared gas grills more efficient so they have fewer BTUs per square inch.
How Many BTUs: In the old days, 100 BTUs per square inch was probably on the low side. These days, grills are more efficiently designed and typically don't need as high an output. For a standard gas grill I recommend looking at how the lid fits to the body. If it is a close fit and the components, like the cooking grates, are heavy the grill should heat hot and fat with a BTU rating of 80 to 100 per square inch. For an infrared grill, the same rules apply but the BTUs should be more in the 60 to 80 range. Of course grills are going to be all over the scale but if you look in these ranges you are probably going to find a gas grill that does its job.
Too High or Too Low: A grill with a really high BTU per square inch is probably hiding something. The lid may be thin, the grates lightweight, or the back wide open. These are grills to avoid. If a grill is low on the BTU range then it will typically have slow preheat and recover times (recover time is the time it takes for a grill to get back up to full heat after you close the lid).