Indeed, there is two important issue in the way you use to distinguish the two polymers.

The first is that the molecular weight of the polymer have an impact on their solubility. The second is, if they are solid and highly mixed, is the possibility of physical interaction between the both product (Van der walls), that can retard or stop the dissolution.

In fact, if you know the molecular weight of the two product, you can found the meting point of each one, and, if they are enough different, you can distinguish by melting this with the lower melting point, or do an ATD.

Hansen solubility parameters are a useful method for predicting solubility. A fairly good introduction to multi-parameter solubiity parameters is http://www.cool.conservation-us.org/coolaic/sg/bpg/annual/v03/bp03-04.html although it is aimed at art preservation. Parameters for your materials can be found in numerous sources, including Hansen's book (ISBN: 0849372488 / 9780849372483, may be in your university library, the 2000 edition is ISBN: 0849315255 and can be had for less than $50: the program is $1100 and includes the book, but this might be a bit stiff.)

The CoOL article mentions the Teas graph, which plots the three paramters on a triangular graph. I've done a preliminary search and found one set of Hansen Parameters for PC, but three sets for ABS. What is notable is that, on the Teas graph, cyclohexane (which has a polarity parameter value of 0 and a Hydrogen bond value of 0.2, ) is in one corner at f_D = 98.8. Methanol's three scaled paramters group around 30%, so it locates near the center of the triangle graph. PC and one of the ABS have parameters which place them about 60/40 (1.5 times further from cyclohexane as from methanol), and nearly coinciding, close to the f_P line. The other two ABS parameter sets place them at roughly the same distance ratio, but closer to the f_D line. According to Hansen's theory, both polymers would have about the same affinity for each solvent.

To get a really accurate readout, you would need to calculate (or make a 3D graph) the vector from the point given by the three parameters for each solvent to each solute, then determine if that distance is greater, equal-to, or less than the R_o (cohesiveness) radius of each polymer. For some types of ABS, methanol maps outside of the R_o sphere and cyclohexane maps inside, which is exactly the same thing that happens with PC. That should mean that both PC and ABS will dissolve in cyclohexane, but won't dissolve readily in Methanol. The ABS sample that Hansen gives in his description of calculation vs. trial-and-error characterization of polymer solubility parameters (Chapter 3, table 3.2, sample U, Hylar(r) ABS from B.F.Goodrich) yields a cohesiveness sphere which does not include either solvent. (But you should check my work, because it was done in haste and by hand.)

It seems that mere solubility is not a sure-fire way to distinguish between PC and ABS.

David Pizon's suggestion is a very good one. You might also review the characteristics of the two plastics and determine significant differences between them which might lead to a more definite method to tell them apart.