Crossover: IIR or FIR?

[Waiski]

Okey, so some data.

Under you see the measurement taken from pre out of D250 Pro. We did check and also speaker output crossover does work the same way.
Measured is fullrange and 250hz 1-4 order crossovers, high pass and low pass.

You can see from the measurements that 1st order crossover does give -3db on crossover freq, 2nd order -6db, 3rd order -9db and 4th order -12db.
So basically Devialet does multiply 1st order crossover 1-4 times. This means that you can use same filter order for high pass and low pass only for 2nd order crossover. Other crossover filters need to be build with calculation I sent earlier.

Order
LP=>-6dB ... -6dB=>HP
HP=>-6dB ... -6dB=>LP
1st 1.733 ... 0.577
2nd 1.000 ... 1.000
3rd 0.765 ... 1.307
4th 0.643 ... 1.556

So for 2nd order crossover you can use this without adjustments. 1000hz is 1000hz crossover point.
But for example 1000hz 1st order crossover point are... low pass is 577hz and high pass is 1733hz.

One of the reasons I got a Devialet was the crossover as I am wanted a digital crossover for my diy loudspeakers. I am using the amp as a for my bending wave design (mids and high) high pass at 400hz and the pre-out for a digital amp driving my woofers. I never measured directly the crossover curves at the amp or pre-out but if I measure my speakers with and without the crossover and look at the difference I get very similar curves except early on the curves were flatter than they should at any crossover slope.
To get a perfect even summ of low pass and high pass they should be -6dB at the crossover point and as the curves show that is only the case in 2nd order. As one can choose independently the crossover frequency for high and low pass one can adjust for a -6dB crossover point at any slope.
Crossover points and slopes are only working anyhow for completely flat frequency response (and than why on would need a crossover).
Because of the slope and rinse of my bending wave driver I get the best results if I an using a setting at 800Hz 2nd order and 300Hz 3rd order for the woofers to get a crossover which sums flat at 400Hz. 
I think to use a crossover correctly measurements are quite necessary.

No need to measure. You can use the calculation I sent. Then you get flat crossover summing. You can use this also to your 3rd/2nd crossover. If you want to have flat crossover at 400hz you put 2nd order high pass to 400hz and 3rd order low pass to 523hz.