A very basic question about response time of an instrument
Response time of a temperature sensor is the time it takes the measured value to get to a certain percentage (in general 95%) of the real temperature when you expose the sensor to a temperature step (for instance you have the sensor at ambient temperature and introduce it in an bucket full of ice).

Your temperature instrument behaves as a first order system. If you review a bit of the theory of these systems and look at the differential equation you'll find out the trade-off for a fast response comes in the form of static sensitivity. For more details you can take a look at the example at the end of this presentation: Sensors and Actuators TU Delft.

There are also quite a number of nuances that you should look at carefully. See, for instance, the thermocouple in a coffee cup example presented here: Dynamic Analysis and Time Response

Now, from a practical (industry) point of view, you should not worry about this particular problem that much, unless you want to measure a fast changing temperature (yeah, I know, how fast is fast?). This choice you have on your device (30ms vs. 300ms, which by the way are not realistic values, in the sense that you would not be able to measure temperature changing at 1/30ms=33Hz) are mostly to help you tune and or stabilize the response of a control system (in case your temperature sensor forms the feedback loop of a control system). I think the difference in between these two time responses is just the corner frequency of a filter at the end of the signal processing stage (this is just my guess, you would have to check with the manufacturer).

If you do need to measure temperature changes at fast rates, then you should start by looking at experimentally obtaining the real response of your whole measuring chain and maybe later looking at ways to compensate it (there is a whole lot of research literature on that topic).