Neither 'filling' nor 'stuffing' is dialect, and neither is restricted to any region. They're both just standard English.
'Stuffing' is material used to pad out the interior of non-foods - sofas, cushions and cuddly toys, for example.
'Stuffing' is also used in the same way for natural objects, either animal or vegetable, that you can eat. If you clean out the cavity of a chicken, a turkey, a pepper or a squash, for example and put something inside to fill it out, this is a stuffing.
We tend to use 'filling' for products that are made from scratch and baked - pies, tarts, puddings, cakes - as well as confectionery such as chocolates with fillings.
And on the subject of sweet things....fillings is what dentists put in your teeth when they drill out the bad bits. Ouch.