Does the choice you make with regard to Tyr make any difference? I just played through both ways, and nothing seemed to change. I know that he says that you'll receive no advantage or disadvantage on the basis of your choice, but I figured there would be differences in the storyline or, after finishing the main quest, the gameworld; however, as far as I can tell everything plays out the same regardless of the choice that you make.
(I should mention I also noticed that after trying both paths, when I reloaded and made the decision to let Tyr live I received an achievement - something like "God Bond" or "Soul Bond", I think - that I had not received earlier when I let Tyr live and played through to the end. This has led me to wonder if other things that were supposed to trigger failed to do so. Unfortunately, I didn't save before loading my finished game to check whether I had received this achievement and have not been able to receive it again after several further attempts.)