Well That really depends. Are Eragon and Saphira in the Elder Scrolls universe? Does that make Saphira a Skyrim type dragon?
Lemme put it this way. If Eragon and Saphira are hamstrung by Skyrim rules Dragonborn wins. If they aren't Eragon and Sapphira win.
For starters Eragon is a mage. Under Brisingr rules a Mage is able to infiltrate their enemy's mind, seize control of their body and kill them with a single word. Ordinarily, wards and the threat of being countered by an enemy Mage helps to balance this power. The Dragonborn, bound by Skyrim's more traditional definition of magic, has no such defences against Brisingr's style of magic.
The fight would be over in seconds. Saphira wouldn't even have to do anything. Without the mental wards or ability to shield his mind from intrusion, which is unique the the Brisingr universe, the Dragonborn would be killed instantly by Eragon with a single word. Especially if this is post-Dragon Ritual Eragon, after he gets turned into a Half Elf. And even if the Dragonborn had the time to get out a Shout, like the one to control Dragons, that Shout only works because Skyrim dragon are bound by that universe's magic. In this case, Saphira is not a Skyrim dragon, therefore Shouts intended to defeat such dragons would have no effect on her.
I'm assuming everyone saying the DB would win hands down are either blinded by their love of Skyrim or basing the fight off of the Eragon and Saphira seen in the movie Eragon.
And don't even get me started on that... Bloody movie was an insult to the books.
Wards exist in the Elder Scrolls universe, though. Based on what we know of wards from Elder Srolls, I would think, lore-wise, they would suffice in countering Eragon's spells. Elder Scrolls also has greater spells that control people- Thu'um has words based entirely on getting your enemy to fuck off, fight for you, and, similarly to Eragon, single words that can just outright kill you.
If we assume the Dragonborn is as most people would attempt to go- a master of all skills, thu'um included- Eragon is fucked. Dragon, half-elf, mage or not.
I can't find much on Eragon's mind powers, but as you said they can be countered with wards, so it doesn't really matter.
Thu'um can be countered with Skyrim wards, but only because those wards also block projectiles, which most shouts are classed as.
However, we're not applying Skyrim logic to Eragon, are we?
