If you use equivalent apertures and the same shutter speed, then the same amount of light will hit both sensors so the shot noise will be identical as well.
Will it?
Yes
Shooting at f1.2 transmits a greater light intensity than shooting at f1.7.
The equivalents are f/1.7 and f/1.3. Spread the greater light intensity of f/1.3 over the smaller area of 24x36mm and you end up with the same amount of luminous power as the lower intensity of f/1.7 over the larger area of 33x44mm. So f/1.3 on 24x36 projects the same light power (which actually hits the sensor) and f/1.7 on 33x44. f/1.2 on 24x36 projects a little more power.
Using the terms as follows:
'Intensity' means power per unit area, otherwise known as 'luminance'. SI unit the lux
'Luminous power' is radiant power (in the physical sense) weighted by the luminosity. Otherwise known as 'luminous flux', SI unit the lumen.
Just to round it out, Luminous power times time gives the luminous energy per unit area, otherwise known as 'luminous exposure', or in photography, simply 'exposure'.
Exposure time area gives luminous energy, which has its own unit, the 'Talbot', after the photographer Fox-Talbot. From the point of view of how much noise is seen in the image, and hence low light performance, it is this that matters.
