Hey, Omur,
These, both, are very small, "mini" strollers so to speak, mainly suitable for malls, airports, holidays, smooth sidewalks. Mostly, they're used for traveling or as a second stroller for the car boot, definitely not as a primary stroller from birth, and it's even dangerous to run with them. Cobblestones will definitely not be comfortable, either, the smaller frames and smaller wheels won't have much cushioning and will often get stuck.
Not wanting to discourage you, if you want it as a second stroller to complement a larger first one, it makes sense, but for running and for more demanding surfaces, like cobblestones also are, go for something larger, and complement it with a travel stroller like this. For traveling, the Mini Buggy Snap will be better as the larger Jackey XL won't fit the cabin luggage requirements. My best advice is to visit a fw baby stores if you have time, check what's out there, and in real life see the size of the whole and the wheels to know what I mean.
P.S. For running, you need a larger three-wheeler, nothing else will be safe enough to use like that. Check the Thule Urban Glide, for example.