The carriages of those two stairs are totally different. This for sure is not a DIY project as it would be really involved, unless your skill level is pretty high, even then it is iffy. Even if code allowed the open risers which it won't. Chances are once the sheet rock is removed you will see the carriage or stringers will not be dressed and several different types of fasteners and bolts will be exposed that would have to be covered, not to mention the holes in the back of the treads where the riser is fastened as well as glue. The scotia mold will leave nail holes on the underside of the front part of the tread also.The front edge of the stringers will have to be dressed someway as well.
Another thing to think of is removing and replacing all of the treads as there will be a 3/4 inch gap behind each tread by the removal of the risers.
Chances are the stairs will be more bouncy once the risers are removed also. You will have to address the exposed edge of the skirts, and if the stairs are mortised in on the wall side, you will have to cover or fill the area where the risers are mortised into the stringer. Even if they aren't mortised in, the skirts will have to be modified and refinished. You will not be able to get that complete open look with the design of the existing stairs.