Functionally, there isn't much difference. The difference really comes down to very small details of each technique, or precisely how the source images for each technique were taken, environment constraints, etc.

Given the following assumptions:

• shooting RAW;
• no movement in the scene (i.e., no heavy wind blowing trees around, etc.);
• zero color-cast of a particular ND filter (i.e., it is perfectly gray);
• zero reflections (or at least no perceptible reflections) caused the ND filter; and
• the ability to create a Photoshop gradient that precisely matches the ND filter's gradient profile;

then exposure blending two shots, say exposed 2 stops apart, will achieve the same results as using a 2-stop ND grad filter and taking a single image.

The differences (probably only very slight, though) come when some of the above assumptions/preconditions are not valid. Probably the most important real-world issue is that all ND filters have some color cast. Of course, if you're shooting RAW, you have the most latitude to correct for it, so it's not a deal-breaker — it's just a known/accepted step in the post-processing of images shot with ND filters.

Personally, I try to get as much right in camera. And I like the whole process of using and working with filters. I don't really like doing a whole lot of adjustment in post-processing, and am not especially good at exposure blending. So my preference is to get as close as possible with the filters. But your mileage may vary. For the mere cost of taking two (or more) bracketed shots, assuming the scene doesn't appreciably change between those shots, you have a LOT more latitude to blend exposure according to your desires, than you do just using ND filters and their rather imprecise blending control.

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Now, as an aside, you also tagged your question with [variable-nd]. Understand that variable ND filters are made by combining two polarizers. Polarizers filter light based on their spatial polarization. That polarization information is not captured by the camera. Therefore, there is no way to identically achieve the same results in post-processing. You can simulate it as best you can, but there is no post-processing that can algorithmically duplicate the effect.

See also:

• Can the effects of a polarizer be replicated in post-processing?
• What types of filter cannot be emulated by post-processing?