Spoilers in this video, big time!
Similarities and differences between the movie and the comic version of Old Man Logan are discussed in this video. As you may have guessed Fox didn't have the rights to all of Marvel's characters so unlike the comic, the movie only consists of X-men universe characters. The movie is less apocalyptic as well.
If you'd like to see the differences for yourself get the book here from Amazon.
If you really want the entire Logan experience then get the western movie Shane here from Amazon.
Shane is a classic 1950's western that plays a part in Logan in a physical and symbolic way. It's a classic movie in it's own right. It's been called one of the best westerns of all time and for good reason.