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Are Troubadours any good at combat/soloing?
Bards are primarily for buffs/debuffs. They can solo, but are not as strong as some of the other pure DPS classes. You'll find they are a very fun class to play, can dual wield, and have great spell animations. They can use ranged weapons, but don't get the large range-damage like Rangers. I use my bow just for pulling.
Swashbucklers are more prone to higher DPS with fast attacks, less buffs.
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Can either class dual wield?
Yes, both Swashies and Troubs can DW.
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Which one gets more invites?
I would say that that it depends on what the group is doing. If a normal exp group, then both can be valuable. If the group needs high DPS, they might lean to the Swashie. If the group needs buffs and have many casters (Troubs have the best power regen skill in the game), they might lean to a Troub.
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Which is "more fun"?
I can vouch for Troubadors, they are very fun to play. They use the typical Scout ability of "Stun/Rear attack". Additional damage is done with songs that are either single target, group, or AE.
Troubs have so many possible buffs, that it's sometimes difficult to decide which one to use. And that's one of the gems of playing a Troub - great versatility with a buff for almost any occasion! :)
You can try both classes and see how you like them.