Everyone likes the big bad villain. Rather, everyone hates the big bad villain. Darth Vader, Voldemort, Sauron– the Dark Lords of fantasy and science fiction have the coolest powers, and most often, the coolest backstories. A normal person would have to go through a lot to become as evil as these people appear. Unveiling that backstory can be more fun than the actual plot, yet accentuate the main character’s story along the way. However, as we understand them, they inevitably become less scary. Darth Vader is just a poor old single father, while Emperor Palpatine gets all the hatred. Voldemort is just a regular guy missing his nose. Sauron… well, he doesn’t have a nose either, but his backstory isn’t so well known.
Sympathetic means feeling the same emotions as the reader, but that has different connotations for villains. It might mean having an understandable path from good to evil (Voldemort style). It also might mean acting in a good way, even though they’re supposed to be evil (Darth Vader style). If you choose not to make your villain sympathetic, they probably still have a backstory that made them that way but you choose not to show it (Sauron style).
All these are viable options, and it depends on the kind of arc you want your villain to have. Do you want a tragic arc, like Voldemort? Or you could have an evil arc that ends in good, like Darth Vader’s. You could also have a slow reveal of backstory (like Voldemort) leading to a good act (like Vader). Or you could have nothing at all, leaving your villain unsympathetic but awesome and terrible, like Sauron.
But that aura of evil is so useful– is it possible to have a sympathetic villain and that aura of evil at the same time?
By nature, the two styles of villain are contradictory. Making the villain sympathetic reduces their aura of evil– the more evil they seem, the less sympathetic they are. (This is, of course, assuming your reader isn’t a megalomaniac.) But all the same, is it possible? Could it be done?
The aura of evil is an emotional reaction to whatever the villain does. If the villain kicks a puppy, the immediate reader reaction is of disgust (exaggerating reactions a little). That reaction is very simple; the villain did this, I don’t like him. The combination of those simple reactions creates the aura of evil.
The sympathy of a character, however, puts a different lens on that scene. As the villain kicks the puppy and the reader realizes he’s had a morbid fear of dogs since his childhood, the simple reaction of disgust is changed to a reaction of pity, or even fear. It becomes a complex reaction– your senses tell you to hate the villain for kicking that puppy, but the backstory puts a different slant on it, changing your reaction. That reduces the aura of evil but strengthens the character in the reader’s eyes.
Essentially, the aura of evil is created by unexplained acts of maleficence; sympathy is created by explaining those acts. The one undermines the other, putting a complex spin on the previously simple emotion. As far as I can see, they cannot be mixed. It’s your job to know which emotion you want most out of the reader. Furthermore, it’s your job to make sure the reader is with you all along the ride– if readers love to hate a villain and all of a sudden, whoops, they were abducted by aliens when they were two, their emotions are wrenched in the opposite direction. If you guide their emotions in the opposite direction slowly, you can create a sympathetic character without jerking their aura of evil away.
Unfortunately, sympathy and evil don’t mix too well. It’s your decision which you value more.