Our Quinny Buzz 3 is very regularly used off road (nature trails, farm, outdoor events), and since a few months has been upgraded with the double tyre at the front. I have noticed differences, but there are pros and cons. I am a motorcyclist, so I would disagree that 4 wheels are an upgrade! Overall, I would say that if the Quinny is likely to see a lot of mostly flat urban territory, the 3-wheeled version is actually better. On bad footpaths and off-road, pick the 4-wheeled version. Another consideration may be that if your baby is small and unlikely to throw its weight around (up to 18 months) three wheels are better, after that a bit of extra stability might be preferred. I found it handy to have both options: 3 wheels around the Trafford Centre and town centres, 4 at forest walks.
Regards the 4-wheeled Quinny.. The 2 front wheels provide better lateral stability. This means that on steep gradients, sharp turns (sharp, steep turns especially) or with a toddler moving side to side a lot, the Quinny is less likely to tip over. Though I didn't find the Quinny Buzz 3 particularly prone to tipping over (its weight centres on the back 2 wheels), peace of mind is worth something. Also, on very poor footpaths and off-road, one front wheel getting stuck in a ditch is less of a problem: putting the weight on the other wheel may set it free. That said, if one wheel becomes muddy the Quinny will pull in its direction much like an old shopping trolley, which is not a problem with the 3-wheeled version. Afterall, one muddy front wheel will resist more, but still go where you point it.
On better footpaths, smooth asphalt and around shopping centres the 3-wheeled version comes into its own. And let's be honest, this is what a buggy like the Buzz is designed for. With one clean front wheel and two at the back, the Buzz turns and handles lighter, allowing for single-finger directional control (yes, really). It also takes up less space at the front than you think, making collisions less likely around narrow aisles, so it's easier to push through. In its triangular shape, it also takes up slightly less space in elevators, in the boot of a car.. And it's negligibly less cumbersome to lift and carry.