The answer to this question is, sadly, not so very straight forward. There are so many variables to consider that the answer will always be up for debate. It is never a "yes/no" question, but one of probability and stacking advantages. Someone can always "get lucky" when it comes to fighting, especially when you introduce weapons into the mix.
As such I will give you a tl;dr of my answer. If it's a purpose built War Scythe, then the longer weapon has an advantage, if it's a common farming scythe then you'd be better off using a long stick. Now on to the details.
The first question you have to ask is, "what kind of scythe are they using specifically?"
If the answer is "War Scythe," then the answer I have to give is this:
The advantage will typically go to the person with the longest purpose-built weapon. The War Scythe even has a treaties featuring them.
If you are using an unmodified Farming Scythe then I will say this:
The one using the sword will likely have the advantage because of the design and characteristics of a scythe which I will go over now.
The most glaring flaw with this farming instrument is the protruding handle on the shaft. It is meant to be held and used in the fashion as demonstrated here and in the picture below.
This means that the majority of pole-arm techniques employed could not be used as they require free range of your hands to travel up and down the shaft of the weapon unimpeded. Here is an example using a spear. Notice the constant sliding of the hands around the shaft of the weapon, a common theme with all pole weapons/long-shafted weapons (though perhaps not to the degree of a spear, obviously).
Also note how the scythe is down low to the ground by default, assuming you are holding it proper grip. This leaves you almost totally exposed on one side, a fatal flaw if there ever was one. You also restrict yourself to the 2, 4, and 6 strikes as seen below.
This means one entire side of your body is exposed to attack with no reasonable means to defend that side.
Some things that it does have going for it is that it would be easy to preform sweeps with it, that is hooking the back of someone's legs and tripping them. Also attacks to the legs, in general, would very swift and difficult to avoid.
I could go on, of course, but this article is getting lengthy enough. So my conclusion is this, the purpose-built tool typically wins. In this case the order of likely hood to succeed is as follows War Scythe>Sword>Unmodified Farming Scythe.