The SASS rules give a significant advantage to 'straight draw' pistols. So, a true 'cross draw' -- where the holster is canted -- is a constant source of irritation, controversy, and in certain situations a real impediment to moving fast.
Many top shooters who are interested in acquiring both pistols with their strong hand from leather have migrated to a modified cross draw where all of the cant is removed from the rig and the off-hand holster is vertical. It's an open question how this affects application of the rules, and probably depends on the individual shooter's movements during transitions. But, most shooters who've gone to this type of rig are very good at re-holstering without problems in all movement situations.
In addition to reflecting on the rules and how that is going to affect your skill development, there is the matter of how your rig affects all four of the transition patterns used in CAS. A true 'cross draw' can impede transitions to the next firearm in at least two of these four patterns. Here again, top shooters have worked out ways for the vertical cross draw rig to advantage them in all four transition patterns and when moving both to the right and to the left during a stage.
You will more commonly find a person who can explain the intricacies of straight draw transitions than you will find a person who can convey the concepts necessary for running a modified cross draw rig. But, if you have an expert at hand who can help you with the issues of using a modified cross draw, then listen to every word they say. Much of their skill in not immediately apparent nor easily understood.
So, to summarize: Don't use a true, canted rig cross draw unless looking good is much more important to you than being good. The most easily understood and efficient rig is the double strong side -- many experienced shooters can help you with the various transition patterns, and the rules afford you great advantage when you use a double, strong side rig. And, finally, if you know an expert who is using a straight draw "cross" rig, ask them to teach you how to use one effectively.
Both the double strong side rig and the modified "cross" rig will prevent you at times from transitioning in an optimal way. Each, in very different movement circumstances. Another way of saying this is that both these rigs can be a huge advantage in certain transitions when moving in a particular direction.
The main problem on every stage is the matter of which hand -- left or right -- needs to be free on the transition to the final firearm. How you use your pistols is one important component of finding a solution to that problem.