This is a question I've been asking to myself from a while, and especially after I saw this video from Thomas Heaton a few weeks ago, where he says that you can get away without ND and graduated filters, but you can't replace a polarizer, as the latter cannot be replicated in Photoshop unlike the other two. And I agree with him for the polarizer, and for the Graduated filters, which is probably one of the few times where I totally regretted buying them. I was excited about those at first, but after a while I realized that they were mostly useless, as you can achieve better results just using bracketing in your camera and using the graduated filter in Lightroom.
But can we say the same for Neutral Density filters? Can just take some photos and then merging them together in Photoshop achieve the same results as a proper filter?

Since I've been started to do long exposures a long time ago, I always used ND filters, first I started with very cheap Cokin filters, which were terrible, very easy to scratch as they were made with some cheap resin, they made any photo on the magenta side, and just forget about sharpness, that one goes straight to the bin. 

Then I tried a variable ND Filter, the Light Craft Workshop Fader ND Mk II, which it did sound fantastic on paper, but again it was just a waste of money, you can read more about it here and here).

After those miserable experiences, I decided to spend some good earned money and get the proper thing, which was the Lee Big Stopper, and I've been rather happy about it, it has some issues, but overall it produce great photos and it's a solid choice in terms of ND filters.

So as you can see, I always used the real thing, and never tried the Photoshop way, and as you can imagine I was a bit sceptic about it, but I wanted to give it a shot anyway, and today I went out to take some photos and compare the results against the real thing.

Now, I'm a total noob for long exposure done with merging shots, and I'm not hiding that I kinda improvised today, light conditions were okay, weather was mostly cloudy, and I decided to shoot in the afternoon just to have stable conditions regarding sunlight, more or less.
Went nearby where I live, tried to find a place near the Dublin Docklands where I could have the typical subjects for a long exposure, some static scene alongside with some dynamic components like water and fast moving clouds.
I tried first with the Lee Little Stopper (6 Stops), but I managed to get only 2 seconds exposure and at f/16 which was the smallest aperture on my lens and I tend to avoid to use that aperture if I can, and still it wasn't enough to see any noticeable movement in the photo, so I put the Big Stopper (10 stops of light reduction), opened the aperture to f/11 and managed to get a 13 seconds exposure, still on the short side, but good enough for a test.

Then to recreate the same effects without the filter, I shoot the same exact scene 20 times at 1/80 of shutterspeed with the camera shooting every second (the lowest interval I could go with the Fuji X-T3), the get the same exposure I got with the ND filter, as usual manual focus and on a sturdy tripod. 
I took 20 photos just to be sure and to have a bit of buffer, but then selected 13 photos, merged into Photoshop using Stacking > Mean to get the long exposure "effect". Down here you can see the result:

Note: One thing I've noticed is that the option to align all the photos messed up big time with the final result, I guess it was because it was trying to align the water, not sure why, but without using the autoalign I didn't notice anything odd and the result seems perfect.

So, now if you compare the two photos you can see a few things:
1) The clouds seems to get the best of this technique
2) The water on the second photo looks less "smoky" and much less smooth and natural
3) The ND filter introduce vignetting where the other technique is vignetting-free, or at least it doesn't introduce extra vignetting apart the natural one from the lens itself.
4) Sharpness is more or less unchanged

After this first test I wanted to try something else, instead of taking a photo every second, I took one every 3 seconds, to increase the long exposure effect, and I took two batches of 48 photos, so 96 photos in total (which I then used to make my first ever timelapse), took one of the two batches, and merged again. Needless to say it took a while to process all these RAW photos.

As you can see the effect is pretty dramatic, 48 by 3 seconds is a total of 144 seconds, with the same conditions of light, I would have needed an equivalent of 13.5 stops of light reduction, which is not that difficult if I stack two filters or I pay more money to get the Lee 15 stops ND filter. 
But again, this confirm that this trick works best with clouds, but with the water of the river stills looks a bit odd to me, better than the first try for sure, but still not as a true ND filter.
As a reference here the same scene shot with the ND filter Lee Big Stopper.

From this quick experiment I can draw a few conclusion, but before let's just sum up the pro and cons of each method.

ND Filter

Pros:

• One photo only and less demanding as a process as a whole
• More natural and smooth results, especially with water
• Done in camera (but this is debatable as a pro)

Cons:

• ND Filters are expensive, especially if you want the good quality ones
• More gear to carry with you and to take care
• Less glass between the sensor and the scene, which decrease of sharpness (but not really a problem with quality filters)

Stacking in Photoshop

Pros:

• No extra vignetting or loss of quality)
• No extra glass in front of the camera
• No need to spend extra money in filters
• Easy to do
• No colour casting 
• No real limitations on how long it can be and more granular control of the final effect

Cons:

• Computationally expensive
• Loads of photo that take a lot of space
• Water bodies and anything moving apart from clouds looks rather unnatural and less smooth compared to an actual ND filter

Conclusions

To be fair I was quite surprised by this test, I was not expecting to get such good results,  and the stacking in Photoshop has a good number of points in favour, the lack of any colour cast, vignetting or quality degradation are factors that you can't ignore, but does this mean that I'll just sell all my filters and start using this technique instead? I don't think so. If you use good quality filters, the sharpness you lose is negligible, colour casting is very easy to fix with lightroom, and even vignetting to some degree, especially if you shoot in RAW (and you should if you don't do it already). But the lack of smoothness, especially on moving objects like vehicles, trees or water bodies, is something that you can't fix in photoshop, or at least not with a few clicks, and while this details are mostly ignored by the common Joe who sees the photo, those details are what make the photo more believable in my opinion.
But in the other hand, if you are starting out photography and you don't want to spend a considerable amount of money just to get some good quality filters, or the photos you take  don't have moving objects apart from clouds, I think it's a perfectly viable alternative, that I might as well in the near future.

As usual I hope that you find this article helpful, and if you have a different opinion that mine, please leave a comment down below.