Sports fans are among the most opinionated bunches of people. We also like dream matchups, often impossible ones. That is why there are endless greatest-of-all-time discussions. In essence, who do you want in your team in the history of the sport if there is THE fight today, even though someone has to be transported from time? In China there is this old saying: 关公战秦琼, or Guan Gong (关公, ~160－220 AD) fighting Qin Qiong (秦琼, ?-638). In the US people are debating whether the 1998 Yankees are better than the 1927 Yankees. It is pure fun to speculate on such fights, hence the Hollywood films such as Rocky 6.
For this fight, we have to imagine that both players must be in their prime. Also, the average levels of play across different eras must be considered, or normalized to be the same. So what we really measure is how much the two players are better than their peer groups.
Suppose men's tennis. It depends on the courts. For red clay, Nadal is the one. Whoever opposing him, does it matter? Any other surface, for me, Sampras or Federer is tough choice. For peak performance, I will choose Sampras. Consistency, Federer is one level above anybody else.
Women's tennis. I will choose Graf. She will have strong competitions though.
Men's table tennis. The field is wide open. Mainly because there are wide varieties of styles that match well with some but poorly with others, also the techniques are evolving. For just one match I will pick Jiang Jialiang, because in mid-1980s he ate Waldner alive, whom many people may pick. But I doubt Jiang would ever be able to beat Wang Liqin.
Women's table tennis. Deng Yaping is the one. She doesn't have the best techniques, but she is fast and furious, and handles players with different styles well. I can't think of any common names capable of a good matchup against her.
Men's badminton. Lin Dan is the one. Nobody else since 1980 comes even half close to his big championship counts and head-to-head records against peer. Opposing him, maybe Yang Yang, with his tenacity, perhaps can rattle Lin Dan. Zhao Jianhua is the one whose techniques and attacking games are the best I have ever seen, but he is not a good defender.
Women's badminton. Another wide open field. Great players at different eras are not much better than each other. I actually think a new comer Li Xuerui, not a world champion yet, may be the one. I like her refreshing style. She is also calm. She still needs to polish her techniques though.
Basketball. Wilt Chamberlain is a player that transforms the sport. He broke
all kinds of records and forced all kinds of rule changes when he
played while never fouling out of an NBA game. Nobody else famous can
claim likewise. Nowadays people talk about Jordan, Kobe, Shaq, and Russell, but
if just a single player, Wilt is the one.
In terms of the record books, baseball probably has the most records documented. Babe Ruth is considered the best ever. Even though his records have since been surpassed by others over times, when he set those records, they were so far ahead of his fellow players, like out-homering every other teams in the MLB and being both an elite hitter and an elite pitcher, that he set a bar so high no one will be able to reach.
Talking about baseball, the biggest story since 2000 is the steroid scandal. On one hand, steroids definitely had an effect. Barry Bonds would not have hit so many HRs so late in his career, which is just against human physiology. On the other hand, there is a lot of hypocrisy regarding players using steroids, like many writers vow not to vote players into HOF simply because of (suspected) steroid use. For one thing, it is not clear how and how much steroid affects performance. It definitely varies among sports. Even in the same sport like baseball, some people may get a better effect, some very little. The argument that steroid use is illegal has many holes as well, because players in earlier years also used illegal drugs, which was already well known then. For what is worth, we had no idea what Babe Ruth took when he was hitting those HRs. Yes, a lot of meat and alcohol, but can anybody be certain that he didn't take steroids or like chemicals? Steroids have been around for a long time, and natural products contain performance enhancing chemicals as well.
In essence, we don't need to know what if. Just two great players relative to their peer groups comparing themselves and the record books.