Fewer (and similarly with Bush’s — both filed a number of lawsuits in the 2000 election), but then, the legal basis of the cases was different.
Its not really anyone outside of the Trump campaign’s (and their legal team’s) fault that the Trump campaign filed an unusually large number of lawsuits making claims that were not justiciable, independently of whether the claimed facts were true.
The Trump campaign filed several lawsuits prior to the election challenging various election procedures--which is how it's supposed to be done--and found mixed success, sometimes winning, sometimes losing. After an election, there is very little legal recourse--even Bush v Gore made it clear that challenging election procedures should be done before an election without very good reason. In the case of 2000, those challenges were largely about various recount provisions, and even then, these were filed very quickly. But in 2020, a lot of the cases weren't filed until previous ones had failed (laches! laches!), and even tried the novel legal theory of arguing the entire election should be thrown out because of a challenge to long-enacted laws (laches! laches!). The lawyers involved changed too--the competent conservative lawyers didn't want to sign on to Trump's crazy legal theories, but Trump apparently decided to not listen to anyone who told him he had no remaining viable recourse.
It is worth pointing out that the defendants in one of the suits have filed a motion to impose sanctions on Trump's lawyers. Amusingly, they ask for a fine of all the money raised for the legal suits, although they are unlikely to get it.