Rp-wise characters loyal or respectful of the Empire/ the law side with Hadvar, mostly for the prospect of him clearing their name. Despite your name not being listed on the executioner's list my characters usually prefer to be safer. Personally, I like Hadvar. He's kind and he's one of my favourite race. and he has cool hair.
I really just go with whoever suits the character best, most often that's Ralof. I dislike the Legion and even though Hadvar isn't as bad as most of them, he's still "one of the enemy" for most of my characters. Also, escaping with Ralof just feels more "right" because he was a prisoner like you, not the guy who was just about to have you executed.
Ah, Ralof is by far the better choice for power-play, but I normally don't loot corpses unless I'm playing a thief, and even then I only take weapons. Another advantage of going with Ralof is that you won't be up against two-handers, so it's easier to fight your way out of that room with 5 guys in it.
It depends on whether I feel like role playing. The first time I chose Ralof and went with the Stormcloaks with the Civil War quest line. After some talking with the NPC's I came to the conclusion that Ulfric was a bit too power hungry than I liked. If I want to play a criminal of sorts, I go with Ralof. If I want to stay good and lawful I go with Hadvar in the hopes of being "pardoned" lol. Either way I join the Legion from now on if I decide to go with the quests.
I've gone with both depending on whether my character sided with the Imperials or the Stormcloaks, but I much prefer Ralof. He reminds me of a lot of people I know - good ol' boy, loyal to family, locally minded. I can't really get behind the Empire, even with all of the drawbacks to the Stormcloaks - in my mind, the Stormcloaks are by far the lesser evil. And I know it's superficial, but Hadvar's French Canadian accent irritates the crap out of me. If he was speaking French, it would be fine, but in English, it grates on my nerves.
Also, I don't know if anyone knows, but if you pick Hadvar, once you get to Riverwood, the iron ingots by Alvor's workbench are allowed to be taken for free. (There's about 9)
You could go on to smelt a few iron daggers to level up your Smithing quicker.
If you pick Ralof they're tagged as 'stolen'.
I've despised Hadvar since I heard him say "Can't wait to kill another one of Ulfric's boys."
This may be a massive double standard, but I hated hearing him say that. The Stormcloaks are his kinsmen, divided by politics and faith, but Nords in the legion should view the Stormcloaks with at least some degree of empathy. On the other hand, I find it easy to justify a Stormcloak viewing Imperial soldiers as the faceless goons of tyranny, and being happy to slaughter them en masse.
I also feel like even a character whose allegiance lies with the Empire would escape with Ralof, rather than remain in the company of a faction which had put them in binds and attempted to execute them. It just makes sense, for survival's sake.
The first time I played, I went with Hadvar because I didn't realize I had options. Now I only choose Hadvar when I'm playing an Imperial supporter or an extremely lawful person who would want to explain himself. Otherwise I choose Ralof because he didn't try to cut my head off!