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In the case of the DM6437 the most efficient way of taking a 720x480 input and generating a 360x240 output would be to use the resizer module in the VPFE. There is actually a good application note with example code that discusses using the resizer here. I am not sure if I fully understood your question, is this the sort of answer you were looking for?
It is possible to have a different input format than output format, you just have to make sure that the transition is being handled in your application properly, the act of resizing the image here is a common step in such format conversions (perhaps the only step with the video drivers handling timing and color space).
I imagine you have a 360x240 LCD attached to the VPBE?