Good question man honestly. 173 wins in a row vs 18 at show of shows. Even if you put it in a different perspective it's like 'what's the bigger accomplishment; a major league baseball team winning every game of the season including the playoffs or winning 18 world series in a row?'. Either way both feats are incredible and statistically and logically speaking, impossible.
Now granted everything is predetermined before hand. Before a match 173 times, they went to Goldberg and said you win this one, 18 times to the Undertaker and said streak continues. But lets get down to it.
The streak is what made Goldberg Goldberg. His streak is what defined the character of Goldberg and made him just a monster in the ring. Undertaker's character was already defined by his very first appearance at Survivor Series '91 before he even entered a Wrestlemania match. Even if it was determined that Goldberg was going to be in a 48 second or 3 minute squash match, he was expected to look tough and unstoppable and find new ways of doing it 173 times in a row which probably got taxing after the first 50 matches.
Now we look at the Undertaker. Nearly two decades of destruction, 18 wrestlemania wins in a row, the retirement of Shawn Michaels and the unprecidented love and adoration from the fans. The Wrestlemania streak has defined the Undertaker's legacy. It will be the biggest reason he gets into the hall of fame, and in my mind it's bigger than ric flair's 16 championships. Going into the Road to Wrestlemania, no matter who else is on the card that night, you know Undertaker's match is going to steal the show simply because the streak is on the line. A streak that Ric Flair, Triple H, Jimmy Snuka, Jake the Snake Roberts, Kane, Randy Orton, or the Great Shawn Michaels, all bona-fide hall of famers, hasn't been able to break.
At the end of the day when it comes down to it, I give 18-0 at Wrestlemania the nod. 173 wins in a row is quite a feat and probably will never be touched again, but then again neither will 18-0. The fact that puts the nail in Goldberg's coffin (no pun intended), is that jobbers and mid-carders and no names were included in those 173 wins. The vast majority were all squash matches intended for Goldberg to look unstoppable. The Undertaker streak was against the top names of the time (yes even Giant Gonzalez, Bundy, Boss Man, A-Train, and Henry because they were being pushed as top card competitors. Also keeping in mind the A-Train match became a 2 on 1 handicap match also involving the Big Show when Taker's partner Nathan Jones was taken out prior to the match. Bundy was a cage match and he was part of Ted Dibiase's million dollar team which gave the concern of outside interference. Boss Man was a part of Vince's Coorperation which also gave interference a concern. Mark Henry was a casket match and was given a HUGE push prior to mania).
Also the bigger fact is 18 and 0 is at Wrestlemania. And at Wrestlemania anything can happen, including ending his streak. A great match is expected at mania whereas Goldberg's matches were mostly squash matches. Plus the fact that Taker started wrestling before Goldberg and is still going strong after Goldberg retired is also a big factor. Good question brother.