With races to 21 it would need to be the first to win 3 sets (best of 5) in order for the total number of games to be roughly equal to a single race to 100. Even better than that is first to win 4 races to 15 (best of 7) or the first to win 5 races to 11 (best of 9), all of which are roughly comparable in length and total games played.
Multiple sets have every advantage and are better for a billion reasons, excitement being chief among them. In that respect it isn't even remotely close. Ninety five percent of the time races to 100 are snooze fests for the entire second half and particularly in the last third with one player being so far ahead that the finish in anti-climactic and lacking any excitement at all. With multiple smaller races the sets are much closer, and until the very last ball falls it will appear that the player who is losing still has a legitimate chance to come back from behind and pull out a victory.
With multiple smaller races you will also see better quality of play because you will always be getting 100% effort from both players. Nobody is going to go into coasting mode, and nobody is going to go into give up mode. In races to 100 it is fairly common for one or both players to not be giving it their all for big portions of the match because they are too far ahead or too far behind.
Multiple smaller sets also put a lot more pressure on the players which further helps to separate who is best. You can never slack off, never think "well I still have tons of time to catch up or mount a come back, no big deal". Every game and even every ball is much more important and much more pressure filled.
Also, if you spread it out over say 3 days as was generally done with the races to 100, most people's schedules don't allow them to watch 3 days of pool, so they aren't going to purchase a 3 day package. And they aren't going to purchase only the first day or only the second day because nobody wants to see just the beginning or something or the middle of something. It would be like only watching only one quarter of a football game. Now they would sometimes purchase just the final third day, since that is the ending, except for by that time 95% of the time somebody is so far ahead that you already know who is going to win and there is no excitement left so you don't end up purchasing the final day either. So they didn't end up purchasing anything at all. Whereas if it were say a best of 9 sets of races to 11, split into 3 days with each day ending after 3 sets have been played, you would still purchase just one single day, even if it were the first or second day, because you get to see a beginning and an ending (you would see three full races placed to completion), and because each of the sets actually means something.