it all depends on what curry, your cooking style, your oven, pans and you...
For instance my ceramic hob can only use stainless steel pans (encapsulated) so if I want to quick/hard fry something I have to put the pan on first for a good few minutes to let the thick base heat up. If I want to do the same thing at my brothers on his gas hob using a thin based wok, its almost instant to get the same effect. So if I wanted to brown some chicken then add onions etc, it would be different depending on pan/oven.
You will also find a difference between similar pans as well, I have 3 different makes of pans (all stainless steel with encapsulated base) but one of them is ve difficult to use to make sauces in as it tends to burn at the bottom unless you contantly stir with a flat spatula to clear the bottom of the pan.
Another factor I mentioned was type of curry, if you are making a Jalfezi its supposed to be hot/quick fried so it would be better in a thin wok type pan, where a long slow cooked mutton curry would be better in a big thick based saucepan/stockpot.
Then comes cooking style and you... if like me you rarely leave something that is cooking, you can constantly tweek, adjust, stir while something is going on. This means I might find a slightly thinner pan great as its quicker to change heat, cooks a bit quicker etc. However if you like to leave things to cook, you might prefer a thicker pan left on a lower heat to gently cook its way etc...
Steve