What is the thermistor sensitivity?

Here it is written:

Some references use the negative temperature coefficient (NTC) a to describe the sensitivity of a thermistor alpha = -B/T².

and here it is

The B constant expresses a degree of thermistor sensitivity (change rate of its resistance) to temperature changes.

Which is common now?

I don't use either one. Both are approximations that vary with the temperature being measured.

I use this equation (or a variation thereof), from the eFunda page,

put this into an Excel worksheet or Mlab code, and compute the sensitivity for any temperature I desire.

Note that you also should consider how you're going to measure the resistance of the thermistor (current source, voltage divider, etc). In the end, you probably care about the sensitivity of the thermistor + measuring circuit, in mV per deg C, or something similar.

$$R_t = R_0e^{B(\frac{1}{T}-\frac{1}{T_0})}$$ Thus sensitivity is $$S = \frac{dR_t}{dT}$$ evaluated in a given temperature point. As you can see, a NTC have a non linear curve, so S will vary depending on temperature.
note The Steinhart-Hart equation: $$\frac{1}{T}=A+Bln(R_t)+Cln^3(R_t)$$ Fits better to NTC curve, so it can be used in a wider temperature range and it has better accuracy