As an owner of a house where some of my CH pipes are running inside the concrete, floor, with bare minimum lagging, I have not had any problems since 1992, that is 24 years and I just hope I have not said this too soon, fingers crossed.
But certainly running them under floor is not a real issue as long as it is done properly, allowing plenty of insulation wrapped around the pipes, preventing any chemicals in concrete from attacking copper pipes, even painting them in thick bitumen layer before wrapping them in some insulating material that also allows it to expand and contract. In another property my cousin ownes, I got my builders to run pipes under floor in a dedicated duct channeled 4" deep and 6" wide inside the concrete floor lined up with treated timber walls to insulate from touching concrete floor, where all 5 pipes run in this channel using spacers at every 1 meter interval, to keep pipes from touching one another or the duct walls or duct floor, and cover made of plywood screwed from top before tiling floor over, so far touch wood that there had been no problems since about 2003, if should a problem occur, it is just a matter of removing a single row of tiles in a straight line to get to this duct. A water leak or gas leak would reveal itself in his cellar as the duct is open at both ends.
Option two is better as it would be more easily accessible should there be any leaks but always remember for yourself where such burred pipes are in case you nail through it or screw something to the wall. If you were having this kitchen/dinner as one, removing the stud wall, you will have to mend the ceiling any way, so might as well get it done through the cavity wall and behind the tiles and through ceiling.