Is there any practical difference with a physical filter?

For the most part, in most typical "I need a 1-, 2-, or 3-stop ND grad filter" scenarios, there's not really a practical difference between the results the filter app can produce and what can be done with a set of ND grad filters.

However, there are some interesting differences, where certain shooting scenarios would benefit with either the app or physical filters.

Where the Sony app wins out:

1. The Sony app can define 3 regions. This is like being able to define a filter's "stop" region (where the full rated filter amount is applied", "pass" region (where no filter amount is applied), and the transition region. With physical filters, you would typically need to stack a ND filter with an ND grad filter to get some amount filtering in both the "pass" and "stop" regions. Or perhaps you would stack two graduated ND filters with opposite transition directions. This app appears to mostly replace the need for multiple ND grads.

2. The Sony app can define the transition regions to "tee" into each other. This is subtle, but this provides a capability the cannot be achieved with graduated ND grad filters. Here's an example from Sony's site:

   
   Sony ND filter app example, by Sony Corporation. Used under fair use for educational purposes.

   Notice how the diagonal line dividing regions 1 and 2 terminates at the line dividing both regions from region 3. That cannot be achieved with physical graduated ND filters.

3. Convenience. This filter app can replace a large collection of ND grad filters, sunrise/sunset filters, reverse ND grads, etc., for most typical uses of graduated filters. This is a huge advantage where you need to hike far to get your landscape or nature shot requiring ND grads.

Where physical filters win out:

1. When you need large ND values, such as when you are aiming for long-exposure effects (smoothing out water, clouds, etc.). For long-exposure photography, in-camera exposure control (shutter speed, aperture, ISO) is not enough. There is simply too much light coming into the lens to rely on in-camera exposure controls, without giving up too much. You can only set ISO so low, and can only stop down the aperture to a certain point (without also trading off depth of field and diffraction limitations) in order to increase the shutter time. This is where 6-, 10-, 13-, and 16-stop ND filters (such as Lee's "Big Stopper" series) come into play.

2. Related to the previous point, if you were to combine a physical big stop ND filter (say, 10 stops) with Sony's ND filter app, you would need to take two long exposure shots (as Sony's ND filter app takes multiple photos with different exposure settings to blend them together).

Not sure which way the advantage breaks:

1. Physical filters mounted on the camera make you look "pro". =) While that is a bit tongue-in-cheek, this has some real-world effects. Anecdotally, when I am composing with filters, I find that people often tend to move out from in front of the camera more often than when I don't have filters mounted. Many times, people confuse the filters with a video matte box, and assume I'm shooting video.

2. People tend to stop and ask questions about the filters. If you like talking to people about photography, this is a bonus. If you don't like the interruption or attention, obviously this is not a bonus. I go either way, depending on how much time I have, how much time I've invested in preparing for a certain shot, etc.