The answer to this is yes and no!
Everyone will have their preferences and you are about to hear about them all. I think that almost any calibre above .243 is ok for stags. What terrain are you on? Also which part of the country, a large Southern stag will take more to ground it than its lighter highland cousin.
In a woodland or forestry environment I would want to use a larger calibre as it should drop them quicker. The chances are with a boiler room shot with a .243 the beast will run on. So, then you have to start looking for the beast.
My favourite is the 6.5x55.
Other goodies will be the .308, .270, 300win mag, 30-06, 25-06, 7mm-08
Choice between .243 and .270 for red stags?
the .270