What base image size to choose to assist easier downsizing? Android applications need image at different resolutions to support different screen densities and pixel size. 

I am planning to provide only one image with high pixel size and let the underlying platform do the resizing. When we shoot an image with a professional camera, let's say I get image size of $5000\times 4000$ pixels. Which is obviously too high for mobile devices. Now to reduce the size of the file (to be bundelled with namtive mobile application) I have two option:


Keep the original image pixel size and perform high compresson at jpeg level 
Downsize the image to more reasonable mobile screen upper limits say $2000\times 1600$ and keep jpeg compression low?


Which option is better quality wise considering target file size to be same?
There is no objectively correct answer, there are too many variables to consider such as the nature of the image you are compressing (how much entropy/how 'compressible'?), how much you would need to reduce the jpeg quality to achieve the desired filesize etc... If it is possible to use a lossless compression format then I would consider that as a solution.

If you want to take an empirical approach you can take some representative images, go through the process of converting them using your two methods, then compare the results. You can use a tool like compare for a qualitative metric or visual comparison.