History has proven again and again that exclusives do not move consoles anywhere close to as well as third party content does. The vast majority of new adopters do so for stuff like Madden, Fifa, Call of Duty.
I'd say it depends on the exclusive. If you simply put up one exclusive against swathes of third party content, then it's a bit of an unfair comparison.
The success of a platform really comes down to the brand, and its perception. This is the most important thing, and PS4 is ahead in this respect currently. But for that brand, there are several pillars. Messaging, content (which includes major exclusives), price, services etc. The image of your brand is very important because it's what drives your messaging. Third party games fall into your content, but big exclusives are also incredibly important. The major issue Xbox One faces right now, on a worldwide scale, is that it's a trailing second place. So the messaging is a bit more difficult, and the brand perception isn't as strong as it was last generation, where it was pretty much the console of choice for the traditional audience (in the US and UK anyway). It's an uphill battle. Your own momentum helps, which is why starting strong is always important.
If you look at the US market alone however, then this is slightly different. While Xbox One is indeed behind, they're quite competitive, and a huge seller like Halo is very significant. We're not talking about exclusives which sell 1 million copies here, although those are important too from an overall portfolio standpoint, but a tentpole title. A title like Halo with a strong marketing campaign is quite significant. That doesn't mean it's going to take the market by storm necessarily, but there's a tendency on GAF to diminish the importance of exclusives. Major exclusives are still significant. Halo may not be as big as Call of Duty in terms of brand, but it's as big as most other major IP such as Assassin's Creed (it's actually a bigger deal than this, but they're of a similar tier), so it's a significant selling point.
The Halo campaign is going to kick in this month though, and they'll make the most of it. Moving into the holidays however, I doubt Microsoft will be trying to sell their console on the strength of Halo alone. This is looking at things at a micro level though. If you extend it to the macro level, then titles like Halo, Uncharted, Gran Turismo, Gears of War become very important. They're tentpole titles with enough selling power, and stand out as differentiators, and can help with brand and messaging. Long-term, this becomes quite important.
For the holiday period in the US, what's going to be important is the price and value battle. If, for example, Xbox One is pushed at $349 with Halo and Tomb Raider, while PS4 is pushed at $399 with Call of Duty and Star Wars, that's a tough battle for SCEA even if they have the two bigger overall brands pushing the PS4. This ties into your messaging and promotion. The additional problem here is that retailers can do individual promotions too with certain things that allow consumers to pick up other titles, so theoretically, you could end up with someone purchasing an Xbox One with Call of Duty, Halo, and Tomb Raider.
Basically, third party marketing partnerships are important, but major exclusives are also quite important, due to the fact that it's a competitive market where both brands are quite strong, so in turn price and value becomes the most significant differentiator. Fortunately, SCEA will be in a better position this year than they were last year, so that'll help.