I think you'll be dissapointed to know that the answer is not that simple
I don't exactly remember it the way i read it, but there's certain architecture differences that complicate things.
First of all, the reason nVidia works so well with tesselation is that it has a load of tesselation-specific shaders in comparison to Ati. On the other hand, Ati handles it a different way, using some general purpose architecture but having lots more of it. The end result? In applications with heavy tesselation nVidia is faster. In applications without heavy tesselation use (or if you turn it off) Ati is faster.
Ati is also cheaper to buy, cheaper to run (less wattage required and runs cooler), more reliable hardware-wise (as it runs cooler) and all around great value. Ati's drawbacks are the fact that sometimes they have "funky" driver support for older games (like it was with IL2 and the unreadable text bug). For DX11 cards today, the main advantage of nVidia is driver quality and marketing/developer connections. Unless someone runs tesselation full tilt and 24/7 (maybe first person shooter games, i don't know) i don't think it's good value for money and i wouldn't buy one today. I might buy one 3-6 months down the line though, if the market shifts around a bit.
I've had both Ati and nVidia cards over the years and i was pleased with both, because i always had cost effectiveness in mind and not brand loyalty. If i was buying a new PC today i would go for an Ati. For as low as 50-100 bucks more than the top of the line single GPU nVidia DX11 cards you can have a dual GPU Ati DX11 card.
Certain benchmarks from the early nVidia 480s showed that comparable Ati models were maybe 5% slower (and that at very high resolutions, it's equal or faster at normal resolutions depending on game/benchmark, ie the differences were negligible) but ran quieter, smoother and cooler. The nVidia cards were still the fastest single GPU cards but being priced so close to Ati's dual GPU models totally defeated the purpose, especially since they needed comparable power (which is a factor if you keep your PC on for long times or days on end, like i do, it shows in the electricity bills) and ran even hotter than them. After all, at the end of the day i'm looking at what kind of performance per dollar (and i mean total cost: buy, power consumption, possible malfunctions) i'm getting, not what kind of performance per GPU
As for wether SoW will use a lot of tesselation, there was such a discussion in the recent update thread. The general feeling is that it will probably be confined to the near-distance LOD models. Meaning, it might be used to render your cockpit but it won't be used to render a railway embankment 3 miles away, until you are flying directly over it and it switches to the near-distance LOD models and even then, i don't even know if it's worth the processing expense when you are zipping along at 250mph.
If this is accurate it's one more reason not to invest in nVidia if SoW is your main interest, as nVidia's main advantage and clear performance lead comes in applications with heavy tesselation use. If tesselation is used just for a bit of touching up and small details, an Ati card will do just fine and save you quite some money to maybe get something else (eg, extra RAM). Also, the new 6xxx series of Ati cards will be on the market in a few months, so we can expect the current models of both nVidia and Ati to drop in price.