There is a usually a very close correlation between the density of the fuel and the heating value of the fuel - i.e. higher density fuel has more energy in direct relationship to it's density.
As KR notes, in the FADEC age, the FADEC is going to run closed loop on whatever parameter it's controlling to at the time (e.g. N1, N2/N3, burner pressure, EPR). Even during transients the FADEC will normally control to "N2(or N3) DOT" - that is the rate of change of the higher pressure rotor speed, or sometimes to 'N1 DOT'.
However there are some exceptions. The FADEC will used max and min fuel/air ratios as a limiter (e.g. fuel flow/burner pressure or similar) for protect against surge (accel) or flameout (decel) - that's why an old, tired engine will accel slower even with FADEC - it'll hit the max fuel/air ratio that the FADEC will allow. And that's where fuel density can come into play since the FADEC is using the actual fuel flow (based on the metering value position), not the fuel energy to determine those limits.
Pre-FADEC, everything was based on the fuel metering valve position, so fuel density would directly affect the accel/decal rates of the engine, and possibly even the throttle position needed for a specific EPR/N1.
There are adjustments on the fuel control units to allow adjustment for different density fuels. They are rarely used outside of the shop unless you're switching between significantly different fuels - e.g. going from Jet A to JP4 or visa-versa. Mechanics will sometimes play with the density adjustment to help an old, tired engine meet the required acceleration requirements, but that is not a recommended practice.