Filters ( of which crossovers are a type ) modify the electrical signal by routing or blocking or diverting certain frequencies and sometimes allowing others. Because speakers are imperfect electromagnetic devices, it is often necessary to route signal to certain devices by virtue of frequency. ( example tweeters can't handle bass frequencies without damage ).
Crossover filters transfer signal at a rate. This transfer rate
is often stated in terms of db per octave.
It is not a matter of a higher slope being intrinsically better: It has it's tradeoffs and design and implementation considerations.
No driver is perfect, so some require that the range of operation frequencies be carefully controlled ( because they would sound bad or be damaged by power )
In the world of Pro Sound - the rooms are bigger and higher SPL and power is required - active crossovers are a practical necessity.
In home audio with lower SPL and power requirement it is possible ( with careful driver selection and matching ) to create successful designs with lower order slopes.
Filters are a complex subject ( entire classes are held on the filter design - been there
If you need some links I can provide some - gimme a clue as to complexity as I have a habit of linking to material from academia which may not help at all.