Both series originaly derive from visual novels by Type-Moon.
The stories are also somewhat similar, both featuring a teenage boy being drawn into a conflict, supported by many female characters, and both series have strong female main characters.
If you by any chance liked the anime of the highly-celebrated eroge game Tsukihime, there's no reason for a person who played Fate/Stay Night to not see the anime. Despite lacking the in-depth story telling present in the games, any fan should at least watch it and compare it to them. Of course that for those who haven't played both games, and loved or enjoyed watching Shingetsutan Tsukihime, Fate/Stay Night should be something they should watch as well. Same universe, different place, different setting. Can you make any connections between both series or their characters?
In both animes the main character is a boy whose life is in danger. Then he gets involved with a girl from another world who becomes his fighting partner. Both animes have quite a sad, serious feeling. Fate/stay night might be a bit more flashy.
Very similar in tone and look. Involves supernatural themes in a vaguely similar way and the male protagonists are similar in their approaches as well. Definitely worth a look.
Based on one of TYPE-MOONs visual novels as well. Written by Nasu Kinoko.
Both by Type-Moon. Almost everything besides the shows specific things seem the same.
When the main male char runs into the vampire princess Tsukihime one day, his life changed drastically. Together with Tsukihime he fights against the evil guy, so in this way it is similar to Fate/stay night. It has also a similar ending.
Although the plot itself has nothing to do with Fate, people who liked Fate usually like more productions by Type Moon, and this is one of them.
Also Produced by Type-Moon and takes place in the same universe
Fate/stay night and Tsukihime plays on the fantasy world on the "modern" era. Fantasy in the sense of monsters and magic, with action and blood.
Animation style, the world in Tsukihime seems a bit more gritty, while Fate/stay series is a bit more vibrant.
From the same creators, Type-Moon
Both based on the erotic visual novel game.
However, they do not use the nude and sex scenes as a crutch in either series. Even though they are targeting the audience of teenage males, the strongest characters are the female leads.
Set within the same universe.