I am from the netherlands and ski in austria and italy since childhood. Will be going to italy Marilleva in a couple of weeks.
Both Italy and Austria have great places to go
First thing to know, do you want nightlife or do not care at all?
Want no brainer it must be Austria.
For a month a car rental is most likely the way to go or go from place to place because you are not likely to stay in one.
To give you an idea i can easily ski the Saalbach-Hinterglemm for a week but a month? to small. But the nightlife is super. But stay away from anything owned by "Wolff". But they do hire people for the ski school speaking english if needed.
Kirchberg/Kitzbuhel is also very nice area
Want to be 100% snow secure go to Solden/Hochsolden or Kaprun to have a gletcher nearby.
Austria is not cheap at all calculate between 100-150 euro (yes that is 150-225 usd) a day for hotel, lift, food and drink. Buy sandwiches at the 711 to have a cheap lunch on the piste and to save 15 euro a day. For nightlife add 50-100 a pop....
Also check the distance to the airport if you are not renting a car. And make sure the car has winter tyres and snowchains, both are mandatory!
Just picking a place between the austrian, swiss, italian border can be fun you can actually ski in all 3 easily on a single day.
You prefer to ski and want better cheaper food not a real beer drinker go Italy
The Dolomitis supersk area is bigger, but again you want a week on one side and one on the other side. It is stretched.
The mountains are more steep overhere much rougher as austria..
You will save on the food, which is cheaper overhere and on the piste usually better as in austria.
You want bigger as that no nightlife, well then france might be it, afaik those are the biggest ones. never been there it is french you know. But the pistes are huge...
Good luck picking a place.