Ahh, an oldie but goodie topic.
Ruth #1, Cobb #2. There is a gap but not a large one imo.
Average - Push, when you consider Babe's approach was power and Cobb's was all BA.
Power - Large edge for Ruth. Shouldn't need to explain. Cobb did very well in SA but that was largely dependent on his legs rather than his power. No insult to not be in Babe's class here. Counting only his full-time playing seasons, his slugging average is .705. As it is, his career .690 is a number that has been reached only 27 times (by non-steroid users) in the history of the game, in a single season.
Arm - Huge edge for Ruth in terms of career. Before Cobb hurt his arm I would just say large edge but Ruth never lost his. It was always top notch. The legs were what went eventually. Never the arm.
Fielding - Positional consideration gives Cobb an edge but not as large as some might think. If we look at his entire fielding career, then Ruth's fielding as a pitcher should be included, and that was very good. Take away those years and replace them with full-time outfield seasons, and his fielding legacy looks much better. Still, Cobb was a very good centerfielder for quite some time before falling off, and he gets the edge.
Baserunning - Large edge to Cobb. Ruth was good to very good and Cobb was excellent.
Off-field considerations - Much tougher for Ruth. The pressure, expectations, and demands on his time, energy, and focus were astronomical. To do what he did day in and day out with a continuous "full-plate" is incredible. When comparing him to Cobb, this is somewhat, but not fully off-set by Cobb's player/manager years.
"The inference is that in the dead of the night the under-secretary of the club owner sneaks to a private telephone, summons the manufacturer, and bids him pour a little strychnine of digitalis into the old apple to make its heart action quicker. The factory gets out the ball bearings, the block rubber, and the go-juice, and the home run epidemic follows." - Paul Gallico