We will use put call parity.This equation is true at every point of option life atleast for european one.
Delta is postive for call and negative for put , so delta is not same
P+S =C +pv(x)
Now if time changes ,then in put call parity right side equation both c (due to theta) and pv(x) changes so to keep the equation valid theta of put must change to nullify effect of call theta as well as change of pv. So theta of put and call can not be same.
Vega and gamma has no effect on Pv as well as stock price. So price change in call and put due to vega and gamma must be same .therefore vega and gamma are same