I have found that as Coles and Woolies modify their house brand offers one then the other can have a better product, and who has the better product can change over time.
For our taste Woolies "boxed meats" (eg prepack precooked like briskets, etc) are better than Coles equivalents. Woolies used to have excellent "Select" unsalted peanuts but has since replaced that line with one that is fairly ordinary, so those are now deuce. Ignoring butchers' offerings, we prefer Coles range of gourmet sausages.
Bottom line is it is good to shop the competition occassionally to see who is really on top for "you", product by product. Brand names are easily compared commodities but house brands change for better or worse over time. In some instances Coles and Woolies carry the same brand but the ranges are not the same, so Woolies might stock A, B, C, and D, while Coles could have A, B, and E, or just A and B, as examples, and vice versa.
Re prices, it seems both Woolies and Coles are playing a good game of selective discounting where the average prices are actually rising, although if one shops the best sales it is good for the consumer.