According to the specs my speakers have 8 ohm impedance with a minimum of 3.5 ohm. By any chance do you know an equation that describes the impedance/wattage/difficulty to drive a set of speakers.
It is complicated, though if you assume everything else being equal, a 4 ohm load will draw twice as much current as an 8 ohm load. The equations you asked about would involve the following:
Ohm's law: V=IZ, or I=V/Z).
Power formula: P=VI*PF, or I^2*Z*PF.
V - Voltage, I - Current, Z - Impedance, PF - Power Factor
Power Factor = Cosine of the angle between the voltage and current phasors (commonly referred to as vectors).
From the power formula, you can see that everything being equal, the 4 ohm load would demand twice as much power as an 8 ohm load. In practice, there are many other factors so everything is not equal. That means a 4 ohm speaker may or may not draw twice (could be more, or less) the power that an 8 ohm speaker does. For one thing, the impedance of a speaker typically varies with frequency and different speakers have different impedance versus frequency and phase angle versus frequency characteristics. As an extreme example, it is possible that certain 8 ohm rated speakers could be more difficult to drive than certain 4 ohm rated ones.
I am mainly interested in the difference between different amp series excluding power output - do manufacturers (generally) improve other components aside from those that are required to handle a larger power output.
Not always, but in many cases, the higher series do have higher quality components in them. The 651A also has at least one useful additional feature, the pre-outs, that allows you to use an external power amplifier. It also has a sub out, though I don't find that too useful, but is an added convenience.