I think that when both players are healthy, Karlsson is a little better offensively and a lot better defensively. Burns is better at shooting for tips but he’s not as efficient as Karlsson at doing so and as you mentioned, Karlsson is far better in transition in all 3 zones. I know Burns had a higher points per game last season but that was pretty heavily influenced by Karlsson’s acclimation period to the team. Even if you want to look at just points, from December 2, 2018 through today including playoffs, Karlsson has 62 points in 61 games, while Burns has 88 points in 93 games.
Having said that, I think there are better methods of measuring offense than raw point totals. If you look at something like Evolving Hockey’s RAPM...
At even strength, Karlsson has a slightly better impact on goals for, and a far better impact on shots for and expected goals for. Karlsson also has a far better impact on shots against and expected goals for, and I think he is pretty clearly better defensively. As has been mentioned, Karlsson is extremely good at breaking the puck out of his own zone and I think that helps get him out of sticky situations. Regardless of how you describe the inputs for their defensive play, if you look at the results/outputs, it’s clear that Karlsson is doing a better job of suppressing shots/chances...
Charts like the heat maps above can be misleading because they don’t account for usage or anything, but these guys both played for the same team, and both guys got pretty similar usage across the board.
On the PP, it’s interesting to see that Karlsson had a weak impact on shots/expected goals, but the thing about those stats is that I don’t find them quite as useful for the PP and the PP is such a smaller sample. By the eye test, I feel that Karlsson is a lot more effective on the PP. His zone entries on the PP are like no player I’ve ever seen on the Sharks, where as Burns isn’t all that good at entering the zone.
Burns arguably provides more value at this point just because he’s an iron man and Karlsson isn’t, but I think Karlsson’s injuries are over blown. I’m pretty confident that a full, healthy season from both players will prove that Karlsson is the superior player.