Oh now I know you are a troll. It would be cheaper to build level intersections with traffic lights. Why then are billions spent on wide freeways, exchanges, overpasses when it’s road over road but when it’s about pedestrians then sure, do whatever is cheapest because they’re already on foot, how much of a hurry can they be in?
Neither. Both cost significantly more to build and maintain than at-grade intersections. That's part of the reason more and more grade separated highways are being demolished and replaced with surface roads.
Yes they cost more than at-grade. At-grade is the most common. I'm talking about high volume areas for both traffic and pedestrians, usually involving 6+ lanes of traffic (even if the roads are at-grade) or a need for foot traffic to cross an interstate where no road intersections exist. These are scenarios where at-grade crossings would be extremely inefficient and probably cost more in wasted time, fuel, etc than the infrastructure cost of an elevated foot bridge. Some places like Vegas have the money to erect elevated foot bridges on the strip even though the intersections are at grade. Of course many places don't need dedicated foot bridges when existing overpasses exist with sidewalks, such as with 676 in Philly.
At high volumes of foot traffic the high cost of sending pedestrians up over a footbridge is greater over the lifetime of a bridge than doing the same to cars.
Consider the physical risks pedestrians takes vs cars over a bridge, the lost time on each journey for cars vs people going over a bridge, fuel costs from additional car trips vs additional fuel cars expend going over a single bridge etc.
Even relatively modest levels of foot traffic pay for a cheap bridge that’s going to last ~50 years.
