Graduated ND filters are better because they have their High School Diploma....

But seriously, graduated ND serve an entirely different purpose than solid ND. And, to be brutally honest, if you don't know the differences, I'm not sure you need or should be buying either.

Graduated ND are usually lighter tints.... one to three stops on the gray side. They are used when part of a scene is overly bright, such as the sky in many scenics. The gray part of the filter is positioned over the sky to "hold it back", making for deeper blue, better cloud detail, etc. Graduated ND are best bought in the rectangular type that fit into a filter holder that's attached to the lens. This allows the filter filter to be adjusted to match the horizon in your scene. (There are round, screw-in grad ND, but those would force you to compose every shot the same way, with the horizon line right across the middle.) Most rectangular Grad ND filters are made of optical plastic.

Full or solid ND come in a wide variety of strengths ranging from one to 14 stops or more. They are used to fine tune exposure, make longer exposures and/or larger apertures usable in brighter light situations... when the camera's native adjustability just isn't enough. For example, one might be used to allow a long exposure that adds some motion blur to an image, such as moving water in a stream or waterfall. Another common use is to be able to use a large lens aperture for a portrait, to strongly blur down the background and make the subjects stand out better. The camera's ISO can only be set so low, and when you're at that limit, the filter reduces the light passing through to allow you to go further. I recommend round, screw-in type filter s

For digital, personally I no longer use my graduated ND filters. I can achieve the same or even better effect with other techniques (such as taking multiple shots at different settings). Graduated ND filters are limited in that they have a straight line of transition across them... yet I rarely have a straight line for a horizon. I can take multiple shots or I can shoot a single RAW and double process it, then combine the "correct" portion of each image into a single, finished image. This is far more accurate and controllable than grad ND filters ever were... I can use the single image/double process technique with moving subjects... and I can use either technique with a wide variety of situations besides the simple scenic shot with a horizon, where no filter would be useful. Also, the oversize, rectangular, optical plastic filters are pretty easily damaged, bulky to carry around and more difficult to safely clean. They also are typically NOT multi-coated and are difficult to effectively shade with any sort of lens hood. Besides, a Circular Polarizing filter is another way to deepen the blue of the sky and IMO, is a much more widely useful filter than graduated NDs.

Solid ND, on the other hand, might be useful if one or the other special effects is your goal (large aperture/shallow depth of field/background blur... or slower shutter speed/motion blur). For still photography, usually all that's needed are one or two fairly strong ND filters.... such as a 10-stop... or maybe a 3-stop and a 6-stop, which also can be used together for 9-stop. The ND filter(s) is use to "shift" the exposure range, which with still photography can be further fine tuned with the other adjustments of the camera (shutter, aperture & ISO). Videography, on the other hand, has less camera adjustability and might require more variety of ND filter strengths to be able to fine tune exposures. Round, screw-in ND filters work fine, since there's no need to orient a horizon line the way there is with Grad NDs. Solid ND also are commonly made of optical glass, will fit under standard lens hoods (assuming you buy the correct size filter for your lens), and are available with multi-coatings that can make for better image quality (and might make for an easier to clean and more scratch resistant).

Finally, there also are "variable" ND. Those are like circular polarizing filters, in that you turn one portion of the filter to increase or decrease it's effect. Many variable ND offer a range such as 4-stop to 10-stop. HOWEVER, variable ND are notorious for having an uneven "iron cross" effect and/or for adding ugly color tints to images. There are higher quality ones, but those are super expensive ($400) and even they aren't entirely free of the uneven effects in some situations. A videographer might want the versatility of a variable ND (rather than a stack of various strength filters)... but it's not really necessary for still photography, where one or two fixed strength will usually do all that's ever needed.

I prefer straight ND filters. Much better pricing, and I don't need an infinite range of filtering. Also, I avoid the dreaded X.

“Only use your Variable ND within its recommended 2 to 8 stop range. If you go beyond the “MAX”, you may experience an uneven exposure or color shift that appears as an “X bar” in the image. This is more common when using higher densities on full frame cameras; however, can be experienced on any camera. This is a common issue– it’s the law of physics when combining two polarizing filters; however, this issue can be eliminated. First, adjust your focal length and then reduce the density (stop value) setting by rotating the filter ring until the color shift disappears.”

http://photography.tutsplus.com/articles/an-in-depth-comparison-of-two-variable-neutral-density-filters--photo-8983

DIY
http://digital-photography-school.com/create-your-own-variable-neutral-density-filter/
http://www.instructables.com/id/Simple-Variable-Neutral-Density-Filter/

Articles
http://philipbloom.net/2011/06/04/the-best-variable-nd-filter-i-have-used/" rel="nofollow" target="_blank">http://www.lightstalking.com/fixed-nd-filter-or-variable-nd-filter/http://philipbloom.net/2011/06/04/the-best-variable-nd-filter-i-have-used/
http://www.learningdslrvideo.com/variable-nd-filter-shootout/
http://nofilmschool.com/2012/12/dave-dugdale-variable-nd-filter-shootout
http://photography.tutsplus.com/articles/an-in-depth-comparison-of-two-variable-neutral-density-filters--photo-8983
http://jonasraskphotography.com/2014/05/12/nd-filter-dont-go-variable/