Both are amazing performers and both have reached a legendary statues in the wrestling business. If your asking in 20 plus years, who will people remember? Well, to the hardcore wrestling fans its obvious people will remember both. Though I feel The Undertaker is a more wide spread name. You could ask anybody who the undertaker is and they'll tell you. My niece who knows nothing about wrestling..hasn't watched a single show of it knows who the undertaker is.
The undertaker has the perfect and most enduring gimmick wrestling ever seen, people love it and eat it up. There's just something about taker that just commands our respect, whether it be the moment the lights suddenly dim and go out and for a few moments people..in anticipation wait in silence only to erupt to the sound of that erry gong that echos throughout the arena which is followed by his the slow mythological dark and spine shivering entrance to the ring..down to the thing he does with his eyes and tongue, it just feels so surreal and it captures and emotion that only taker can bring. You know your in for something memorable when takers on the card or even just makes an appearance.
HBK is an icon,hes the showstopper,the legend,mr Wrestlemania. What ever you want to call him, you might as well just say HBK is a wrestling god(Sorry JBL) hes been the top of the mountain and has put on more 5 star matches than most people will in their entire careers. Hes a decorated champion and is loved and respected by all. He was able to come back from what people said was a career ending injury and still out preform half the roster..even leading into his retirement days. Just like Taker, when ever you seen Shawn on the card..you knew you were in for a roller coaster ride. Sure hes captured more titles than Taker, but taker has never really needed a title to get over, he was always over.
From a wrestling stand point, its hard for me to say. Both are amazing in the ring. HBK is without a doubt the more athletic of the two but that's not to say Taker is a slouch in the ring though. I've never seen a man like taker jump over top ropes as high and far as taker could. Both are amazing at what they do, put them together and you get something special(as we've seen). So both are amazing, but I think Shawn has the edge in this case. Not to take anything away from taker hes just as amazing.
On the Mic I would also say Shawn is the better of the two. Undertaker seems to stumble over words sometimes but I always loved a taker promo of taking your soul and what not. Its always good for nostalgic reasons. Shawn knows how to draw of the energy of the crowd and use it to deliver any kind of promo you can think of. Taker doesn't rely on trying to capture an emotion. As far as his gimmick goes, he doesn't have any.
However, like I have mentioned before, undertaker brings a type of presence with him that just makes the hairs on the back of your neck stand up. Taker has, and most likely will always be a draw. People love seeing him, they love to cheer him. The Undertaker could tombstone a basket of baby kittens and the crowd would just go nuts. HBK is a draw no doubt but I feel hes not quite on the same level as taker in terms of being able to draw a crowd.
Overall I think both are equal and amazing in their own rights but some aspects are a bit over shadowed by other abilities but their almost far to minuscule to even notice. A lot of people have said HBK. So I'm just gonna go with The Undertaker just because I've always like him a lot more. So that makes me a little biased but whatever. Both are pretty equal once you break it down but there both great in my mind.