I think the commonly held theory is that the sunrise is more important. The sun rising on the solstice would be the signal for a collective sigh of relief after months of nights getting longer and temperatures dropping it would signify that the sun was still gonna come up and not just slowly fade away.
Many megalithic 'burial' monuments are aligned on the midwinter sunrise and there's the 'Stonehenge is a midwinter monument' theory too.
The fact that the sun rises in the same place for a few days would be terribly useful as, if it was cloudy, you got a few more chances. Maybe if it was cloudy throughout this would be a 'bad omen'...
What with the year not being exactly 365 days it would probably be a useful 'reset' as well for measuring time...