Different size sprinkler bulbs on a sprinkler head in the same room.

A couple reasons:

1. QR are required per 13 to be installed in all light hazard areas
2. QR sprinklers will respond before the SR will. The intent is the sprinkler(s) closest to the fire to deploy first for fast suppression.

I'm sure others will have more.

As stated, QR is required by code.
Second, their use allows us to employ different design strategies such as area reduction and the like.
The entire purpose of a sprinkler system is NOT to put the fire out. I have not seen a sprinkler than can accomplish overhaul.
They are there to hold the fire in check until professionals arrive. The faster they operate, the better. So, lower temps, quicker bulbs.
Light Hazard fires do not generate much heat in the scheme of things. So the smaller bulb operates much faster.

You should investigate R.T.I. (Response Time Index)

R/
Matt

Here it states the Response Index Time in NFPA 13 2010 edition
3.6 Sprinkler Definitions.
3.6.1* General Sprinkler Characteristics. The following are
characteristics of a sprinkler that define its ability to control or
extinguish a fire. (a) Thermal sensitivity. A measure of the rapidity
with which the thermal element operates as installed in a specific
sprinkler or sprinkler assembly. One measure of thermal
sensitivity is the response time index (RTI) as measured under
standardized test conditions. (1) Sprinklers defined as fast response
have a thermal element with an RTI of 50 (metersseconds)
1/2 or less. (2) Sprinklers defined as standard response
have a thermal element with an RTI of 80 (meters-seconds)1/2 or
more. (b) Temperature rating. (c) Orifice size (see Chapter 6). (d)
Installation orientation (see 3.6.2). (e) Water distribution characteristics
(i.e., application rate, wall wetting). (f) Special service
conditions (see 3.6.3).

In light hazard occupancy such as an office space quick response sprinklers operate and react to fires faster than standard-response sprinklers. The fast response time often results in improved sprinkler system performance. Fast developing fires with large heat release occur in extra high hazard occupancies were standard response sprinklers are more common. This occurrence can open a large number of quick response sprinklers before the sprinklers have time to control the fire. The large operation of sprinklers in a short period of time can overtax the system.

I hopre I'm getting it right?!