As expected the Snapdragon has better battery life. It lasts 13.2% longer than the Exynos in their battery test (9:45h vs 8:28h) with the biggest differences being in calls over an LTE network (34:15h vs 28:26h) and video playback scores (11:27h vs 9:16h). The Snapdragon version is superior in their web browsing and gaming sections too.
There's surprisingly not much of a difference in performance with the Exynos version getting slightly better Geekbench scores. It's also a smidge better in the GPU stability test. However the Snapdragon version pulls ahead in the GPU tests and throttles slightly less in the CPU stability test.
With regards to the camera, it seems like the Snapdragon version produces sharper images.
With Samsung dual sourcing SoCs next year it's clear there are going to be significant differences since different foundries are going to fab both chips for that generation. The difference in battery life should be even bigger with the S24 as the Snapdragon version will be fabbed by TSMC who's process is superior to the 4nm LPP+ that will be used for the Exynos 2400. There's also history of the Exynos version performing poorly at launch.
Unfortunately both chips were fabbed by Samsung Foundry. Tensor is also fabbed by then which explains the overheating, poor efficiency and throttling. I really hope Samsung can catch up with TSMC with 3nm but would be wary of a Samsung fabbed SoC until they prove they've caught up. Qualcomm moved from Samsung to TSMC for the 8+ Gen 1 because Samsung weren't meeting their targets as they had low yield. The yield issue seems to be fixed according to some media outlets but doesn't seem like the fab itself has improved.