Well Hristjan, is this just a general question or are planning to DIY (Do it yourself) as in make your own crossover?
There are a lot of things to consider when building your own speakers. My suggestion is this: Think about what exactly you are trying to accomplish and come back with a more specific question.
Using first, second, third or fourth order filters and crossover points are among the many things that will effect sound quality.
Hopefully, you'll answer my questions and someone more qualfied than me will have answers. Be prepared to answer more questions though.
The crossover filter largely determines the frequency response of each driver within the system. There are various types of passive filter networks which can be used when designing a specific filter order; i.e. Butterworth, Chebychev, Linkwitz, etc. "Filter order" would be; first, second, third or fourth. The apparent roll out/roll in of each filter order is 6, 12, 18 and 24dB per octave with first order filters being the most shallow and fourth order being the steepest. How well the crossed drivers work together is largely determined by the crossover order and the mechanical limits of each driver. Employing first order low pass and high pass filters on a two way system risks allowing too broad a frequency response from both the low frequency and the mid/high frequency driver with poor integration of the two combined drivers. First order filters tend to require very high quality (expensive) drivers which do not have serious out of bandwidth problems. A first order low pass filter employed at 150Hz to a woofer would still allow the driver to have significant output well up into the 4-500Hz range unless the mechanical roll out of the driver limited its output. A first order high pass filter aimed at 2kHz would still have quite audible output down into the 7-800Hz range which is well beyond the normal operating range for any decent tweeter.
Each filter type is selected for its specific qualities such as being "transient perfect", "phase correct" or "time perfect", etc. Oftentimes, the specific type of crossover filter selected will result in a specific dispersion characteristic of the speaker system resulting in a correct placement of the speaker system being determined by the crossover characteristics as they refer to the "lobing" of the drivers. Pay no attention to the correct placement height of the speaker system and your ears and the result will be inferior sound quality.
The existence of a crossover implies the use of more than one driver so the crossover would also affect the time and phase components of the complete speaker system and, as mentioned, the transient characteristics of the system. Due to the phase shift charcteristics of each filter order and type, one driver's output will inevitably lead or follow the output of another driver which might easily result in audible smearing of numerous sonic qualities such as detail retrieval or accurate soundstaging. More gross effects might simply be a honky, muddy or nasal quality to the sound if the drivers are not well matched to the filter characteristics.
Additionally and probably most importantly, a passive crossover's electrical components are a major contributor to the overall impedance curve and electrical phase angle of the speaker system in total. These two qualities are going to have an interaction with the amplifier driving the speaker. If the amplifier is not compatible with the speaker's total load, sound quality will suffer. Therefore, the crossover is that portion of the speaker system which makes for a succcessful match between amplifier and speaker and can, if mismatched, result in very poor sound quality or, if well matched, quite satisfactory performance from the system as a whole.
An active crossover has few of the same problems as will a passive filter since the active device is running at line level and placed in front of the amplifier rather than at speaker level after the amplifier.