I think they're different artistically, but as far as their egos go, they're quite similar. Taylor does a better job of hiding her ego, but it's evident in the image she creates for herself. She makes herself out to be flawless, beautiful, somewhat goddess-like. The only major difference is that Kanye let's people KNOW that he thinks he's a flawless god-like being living among the humans...
Taylor Swift and Kanye West both enjoy the spotlight and performing in front of a crowd. While Kanye receives attention for his outlandish statements, Swift receives attention for her love life and sharing those experiences in her songs. Both Swift and West are considered leaders in their respective genres, attracting fans and paparazzi alike.
Taylor Swift and Kanye West are masters of promotion. Swift's op-ed piece in the New York Times recently was hailed as brilliant, but was really part of the lead-up to her new album cycle. Kanye knows his marketing timing perfectly. He knows when to spout off, and when to back out when fans and the media are getting sick of him. It is still amazing that they haven't done their duet yet. It will happen - there is too much money to be made.
I have seen instances online and on GIFS where Taylor has been caught in an unflattering manner. One example is when she automatically assumed that she won the Oscar for best song and started getting up and then realized it was actually singer Adele that won. Another is her snide comment referencing Harry last year when she won and MTV award.
Artistically they are very different. Their style of music is polar opposite to each other. They do both have large egos and think they are a lot more talented than they are, and they try to get a lot of attention on themselves, but I can't see other similarities other than that one.