Is there a difference between a bad aluminium and copper connections (everything else being equal?)
Yes, aluminium and copper and different materials with different properties, and this can have an affect of the failure mode of a connection.
Copper has a melting point of about 1050°C, whereas aluminium melts at about 660°C. This is a major factor in the failure of a connection, as aluminium has a lower melting point it will typically fail much earlier.
Copper oxide is itself fairly electrically conductive, whereas aluminium is resistive. This means that once oxide begins to form on equal components the aluminium connection will have a faster increase in resistance, and therefore it should fail faster. Aluminium also oxidises very fast, compared to copper.
Copper is a soft metal, this means that it compresses well, and we often rely on compression to make a connection. Aluminium however is harder, doesn’t compress well and is more difficult to get good connections with.
I have always considered a bad connection on an aluminium conductor to be “Critical” at any level, regardless of its temperature or ΔT.