Pre Amp vs Crossover , What's the different ?

I want to build a 2-range speaker system (treb and sub). I came across 2 circuit diagrams. One uses a preamp to filter out the frequency and then connects to the amplifier.The other one does this using a crossover.

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What is the difference between a preamp and a crossover when it comes to filtering out the frequency?Which one would work best in a small speaker setup?

My setup:
Amplifier: Tpa3116d2
Woofer: 4ohm - 20w
Treb: 4ohm - 15w
 
With one more addition, active crossover on picture is not replacement for passive crossover on second picture.
This active crossover only separates sub frequencies from full range L &R out. L& R out still have all frequency on it's outputs. Passive crossover on second picture separates highs and lows on each output.
 
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Furthermore, any active circuit quickly becomes more complex in case -in addition to "plain" filtering- equalization of midwoofer peaks heave to be dealt with. In passive a simple LCR circuit will do that, in an active circuit you need some form of a notch, e.g. a gyrator notch, twin T, Fliege, Bainter or whatever citrcuit. Advanced active is not for the faint of heart or absolute beginners. The circuit attached is from the Linkwitz Orion speaker, containg a number of equalizing networks.
 

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With one more addition, active crossover on picture is not replacement for passive crossover on second picture.
This active crossover only separates sub frequencies from full range L &R out. L& R out still have all frequency on it's outputs. Passive crossover on second picture separates highs and lows on each output.
Thank you for pointing that out, I have to find a treble circuit to make my setup work
 
One more thing to point out re Linkwitz: the boards he designed left “options open” so he could use the same boards for different versions of his products. So while a fully developed active crossover isn’t a beginner’s project, the final product might not be as complicated as this Orion schematic would suggest; Linkwitz wouldn’t necessarily have used all the features in a particular product he allowed for when he designed the board.
 
The first schematic, the two way, would be a very good starting place if you want to build an active-crossover system. The very first thing would be to choose a crossover frequency that’s well within both the high frequency range of your woofer and the low frequency range of your tweeter, and then gain confidence in calculating the R and C values needed to realize the filters involved.

Or, instead of working with physical boards and components, you could use a digital signal processor like one of the MiniDSPs, that make it very easy to realize various filter responses like this basic one and then ever more sophisticated ones as your knowledge progresses. And that would be your crossover. Enjoy! 😀
 
Or, instead of working with physical boards and components, you could use a digital signal processor like one of the MiniDSPs,
Yes, the flexibilty of DSP or an adjustable analog active crossover unit is very helpful when going 'active'.
They allow for easy adjustment of the crossover frequency and output levels for each driver, which is more difficult to do with passive circuits..
The flexibilty is important because, you may start with some design values based on driver data sheets and simulation software, but where you end up is likely to be different, after actual listenening tests, in your room, with your sound and musical preferences.
The goal is create a system that you enjoy listening to.