Personally I would use the A8. Many of the roadworks have been finished, but they are upgrading it in sections so there will be contraflows for some time (2-3 years). Too much of the A3 is still two lanes, and it's a drag with all the lorries that use it. The traffic is usually heavy around Stuttgart and Pforzheim. You could take the A9 to Nürnberg, then cut across the A6. We used the A6 in May and it wasn't too bad. I suspect that most of the traffic will be heading south on Saturday. Another tip: take the Achenpass road past the Achensee, you might think the motorway via Rosenheim will be quicker but the A93/A8 junction at Rosenheim can clag badly, as can the A12 past Kufstein.
TBH, it's a Saturday, it's holiday season, it's not going to be any fun whichever way you go!
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