This one, for me, is extremely easy. As much as I love The Undertaker, Shawn Michaels wins this one in a landslide.
Within 1 year of his debut, The Undertaker defeated Hulk Hogan for the WWE title. However, his reign lasted only a few days, before he gave it back to Hogan, and he never tasted ANY gold for another 6 and a half years. During this time, I do not recall him being anywhere near the Main Event on a consistent basis. His WrestleMania Matches between the title reigns were against Jake Roberts, Giant Gonzalez, King Kong Bundy, and Diesel, and he was left off the card for WrestleMania VIII. He also was not considered a very good worker during this time, which was why he wasn't in the Main Event/Title picture. After regaining the title in 1997, he got it back in 1999, and then 2002, and he has been a Main Eventer and a good worker ever since, winning the 2007 Royal Rumble and 2 World Championships (1 in 2007, 1 in 2008)
When The Rockers came to WWE, they were arguably one of the most popular Tag Teams in quite possibly the strongest Tag Team division in WWE history (oh how I miss those days). When Shawn Michaels became a singles wrestler, he really didn't stumble, winning the Intercontinental Championship, and stealing the show numerous times at big events (i.e. WrestleMania X, where he wrestled a Ladder). He was 1/2 of quite possibly the greatest wrestling match of the 1990's (WrestleMania XII vs. Bret Hart). After winning Back-to-back Royal Rumbles, he won the title at WrestleMania XII. When he won the belt, he immediately became the backbone of the company, and carried the company for the next 24 months, being the Main Event with or without the title. At Royal Rumble 98, HBK broke his back (ironically again against Taker), and he "retired" at WrestleMania XIV, putting over Stone Cold Steve Austin (how he was able to wrestle with a broken back is beyond me). After being away for 4 years and 5 months, he had a "1 night only" return against Triple H, and if you didn't know he was out of action 4.5 years, you couldn't figure it out by watching the match, because he was as good, if not better then he was in the late 90's. In November, he won the World Title, and after losing it the next month, went on to steal the show (did you expect anything else from him, really?) at WrestleMania vs. Chris Jericho. Since then, he has returned full-time, and he has been in the Main Event picture (granted he hasn't won the title again) the entire time. He also has put on phenomenal bouts with the likes of Chris Jericho, John Cena, Triple H, a 60 year old Ric Flair, a 60 year old Mr. McMahon, and a 50+ year old Hulk Hogan, as well as anybody else (he could probably have a phenomenal match with a pile of monkey crap).
Undertaker advantages over HBK:
Longevity without extended hiatuses: Taker has taken time off, but never for longer then a year, while HBK missed 4.5 years.
Ability to adapt character: Undertaker became a biker for 5 years, while Shawn Michaels never really changed his character drastically (he has had subtle changes, such as no longer being an obnoxious prick on TV)
HBK advantages over Undertaker:
Quality of work: The Undertaker, while getting better in the ring, cannot hold a candle to Shawn Michaels as an in-ring worker.
Ability to Steal the Show: Has anybody ever said "wow, The Undertaker really stole the show tonight?" I don't think so. Has anybody ever said "wow, HBK was not good tonight?" No they haven't, because they can't, since HBK never seems to have a bad night (his version of a bad day if he has them is considered a good day for most workers).
Ability to carry the company: HBK carried the company on his back single handedly for 2 years (which made him breaking his back literally rather ironic). Undertaker has never done that.
Both of Undertakers advantages are not really that drastic (Taker has probably missed around a total of 3 years because of injuries, and HBK never really needed a drastic change of character). Meanwhile, HBK's 3 advantages all equate to being better then Undertaker. Thats why it isn't even close, the answe HAS TO BE
THE HEARTBREAK KID, SHAWN MICHAELS
ps: as I said before, I love the Undertaker, and this isn't a knock on him. Taker got an impossible draw in my opinion here, because I don't think anybody is better then HBK.