I'm not sure about the term "cross bike", which doesn't seem to be used in English-speaking countries (except as an abbreviation for cyclocross, but that's not what this bike is); perhaps it's what we call a "hybrid bike" (although hybrids usually don't have a suspension fork)
Cyclocross bikes are a totally different category. They are intended for racing, and are basically road bikes ('Rennrad' in German) that can accomodate wider tires (usually up to around 40mm, although cyclocross racing only allows up to 33mm). Usually the rider's position is slightly more upright than on a pure road bike.
A suspension fork is only useful for bumpy trails with rocks sticking out of the surface. In my experience, they don't absorb tiny bumps (like gravel) or vibration. Unless you are riding on bumpy singletrack trails, a suspension fork doesn't do much. What makes the most difference for comfort is the size of the tires. Wider tires (35mm, or better yet, 40mm) absorb a lot of small bumps and make the ride a lot more comfortable. This is mostly because you can run wider tires at lower pressure, whereas narrow tires need high pressure and tend to feel rock-hard. The tires on the cyclocross bike you linked to are 35mm, which is pretty decent, but 38mm would be better. Maybe that bike can accomodate 38mm or 40mm tires, which would be good.
A lot of people are under the impression that some frames have magical properties that allow them to absorb vibration, but in my experience this is just wishful thinking. There may be a difference there, but it is tiny compared to the difference between thin tires and wide tires. Tire pressure makes a much bigger difference, with lower pressure being more comfortable.
You also asked about handlebars and lower gears. I used to ride only mountain bikes and have recently started riding a cyclocross bike. The more leaned-over position (lower handlebars) on the cyclocross bike is less comfortable and I'm getting a lot of pain in my shoulders and neck. However, the drop bars allow multiple different positions for my hands, which reduces pain in my hands on long rides compared to my mountain bike.
If you ride steep hills, you are going to miss the lower gears of your old bike. Unfortunately, the cyclocross bike you are considering has an 11-28 cassette and a 46-36 crank, which means that the lowest gear is 36/28 = 1.28, while your old bike had a lowest gear of 26/34 = 0.76. That is a huge difference !
The advantage of the cyclocross bike is that the drop handlebars are more comfortable for your hands on long rides (more than 2 hours) and you can go quite a bit faster due to the more aerodynamic position. My mountain bike with slick tires is very similar to your old bike, and I used to go around 16-17mph on that bike. With my cyclocross bike, I can usually go 19-21mph with similar effort. I'm just hoping that the pain in the shoulders and neck will go away as I get more used to this bike.
Bottom line: if you really enjoyed your old 'cross' bike and are concerned with comfort, then a cyclocross bike is probably not a good choice for you.