As is noted in your answer, the mechanics here are pretty clear:

• The vampire takes normal damage from Sunbeam (6d8, with the option to repeat on subsequent turns) and Sunburst (12d6).

• In the case of Sunbeam, the vampire takes an additional 20 damage at the start of its turn, if within the 60-foot radius.

The vampire doesn't take extra damage from Sunburst, because there is no sunlight at the start of its turn. Simple enough.

Which is "better" depends on the situation. 12d6 will generally do quite a lot more damage than 6d8, but 20 damage / round narrows the gap almost immediately.

This does mean that in this particular instance, the level six spell may be a bit better suited to the situation than the level eight spell. Never fear, the eighth level spell will usually be a lot better (hits more targets for more damage, does other useful things).

Mechanics vs. Flavor

The mechanics above are pretty clear. But the mechanics may not fit the lore you have in your head about vampires (I think this is what SSD is getting at with his comment). As the DM, you have two options here.

1. Fit the lore to the mechanics

   The first is to fit the lore to the mechanics. Here, it's pretty simple... Vampires burn in the sunlight, but it takes a little sizzling before they start to hurt. Sunburst just doesn't shine the light on them long enough to cause problems (other than, you know, the massive amount of radiant damage and potential blindness).

   A longer dose of sunlight gradually sets them on fire, triggering their weakness.

2. Bend the mechanics to fit (your version) of the lore

   Sunlight hurts vampires, right? So go ahead and throw an extra 20 damage onto Sunburst. It's not the rules, but if it makes the fight more fun, then that can be fine.

Which you choose will depend on your group, and how often you bend things in their favor ("hey, 20 extra damage!"), vs. how often you bend things against them.

The designers don't think this is an issue

The Monster Manual for D&D 3.5 in its glossary entry on Spells included this:

A spellcasting creature that lacks hands or arms can provide any somatic component a spell might require by moving its body. Such a creature also does need material components for its spells. The creature can cast the spell by either touching the required component (but not if the component is in another creature’s possession) or having the required component on its person. Sometimes spellcasting creatures utilize the Eschew Materials feat to avoid fussing with noncostly components. (315)

…Yet similar text is absent from the Bestiary for Pathfinder. So this became kind of a big deal, discussed at length in a 2010 Paizo messageboard thread. In that thread, creative director James Jacobs eventually says in this post that

For humanoids, somatic components include hand gestures. For things with other shaped bodies, somatic components include whatever gestures their body naturally makes, be that paw or leg movements, tail wagging, squirming bodies, or whatever.

…And the thread is shortly thereafter locked, the matter considered resolved by the Pathfinder staff.