Over 100 people are part of the Drama Desk organization (not a huge amount, but still) and to be a bit more competitive in a way, the awards include Broadway, Off-Broadway, and Off-Off Broadway.
For the Drama League, only one single performer (play OR musical) can win each year, and a person cannot win twice in a career. Pretty competitive!
But in any case, there is often a lack of overlap, and winners of Drama Desk occasionally aren't even nominated for Tonys. It's kind of like the Golden Globes vs Oscars in that respect, but it can often be seen as a bit of a predictor for Tonys.