"Will programs that didn't work with Vista but did work with XP work in Windows 7?"

Windows 7 is a lot like Windows Vista under the covers. So, in general, programs that run fine in Windows Vista will run fine in Windows 7. That also means that, in most cases, those programs that did not run in Vista also won't run in Windows 7. There are a couple of exceptions. In particular, Microsoft has done some work to "rescue" certain applications that did not run in Vista so that they can indeed run in Windows 7.

Microsoft has also added an "XP Mode" to some versions of Windows 7 that allows programs that won't run natively in Windows 7 to run via an XP virtual machine. XP Mode does require more memory as well as a machine whose processor has hardware support for virtualization, something many older machines and some current machines don't have.