No, way different.
The primary theme of this film is the Meiji Restoration, and the waning days of the Samurai, and their control over the Emporer. Prior to the events in this film, Japan was ruled by the Tokugawa Shogunate, and the Daimyo, in essence, the Samurai class ruled Japan right up until Meiji came to power.
Shogun is set nearly two hundred years before the Meiji Restoration, when the Samurai influence was absolute, and Japan was little more than several small countries ruled by individual Shogun. While it deals with a similar setting (east vs west) it is really more of an observation of how Blackthorne saw and tried to adapt to Japanese culture. Shogun BTW is based on the life of William Adams, shipwrecked in Japan in 1600. He had managed to impress Shogun Tokugawa Ieyasu with his seafaring knowledge and was made an honorary Samurai and granted a large estate.
In terms of what the character go througth, i.e. adapting to Japanese culture etc love stories are there any similarities between Shogun and The Last Samurai?. I've purposly tried to not to find out much about The Last Samurai so it is all new when I go to see it but from what I have seen, these character themes and story's are what seemed similar to me (not the setting and historical aspects), is this the case or did you find it quite original?
Also have you read/seen Shogun and seen The Last Samurai, if so which did you refer and why? cheers!