This tutorial provides the modification which moves the featured image after the entry title in the Genesis Featured Posts widget.
Tested using the Magazine Pro child theme by StudioPress however will work in any Genesis child theme.
This solution requires the use of the code in this tutorial which enables you to modify the default functionality & markup in the Genesis Featured Posts widget.
Once you have access to the download folder, follow these 2 steps :
Step 1 : Upload the folder named widgets to your child themes root directory.
Step 2 : Copy & paste the PHP code from the functions.php file to the end of your child themes functions file.
Register or login to access the code in the download folder :