There can be no doubt that active is better and substantially so. Personally I wouldn't use digital filtering though.
Crossovers for active speakers can be built passive of course... which is usually ignored.
The main reason active is not used more widely (by amateurs anyway. It's the norm for professional studio monitoring) is "audiophile disease".... it rules out tinkering and box swapping!
Arkless Electronics-Engineered to be better. Tel. 01670 530674 (after 1pm)
Modded Thorens TD150, Audio Technica AT-1005 MkII, Technics EPC-300MC, Arkless Hybrid MC phono stage, Arkless passive pre, Arkless 50WPC Class A SS power amp, (or) Arkless modded Leak Stereo 20, Modded Kef Reference 105/3's
ReVox PR99, Studer B62, Ferrograph Series 7, Tandberg TCD440, Hitachi FT-5500MkI, also FT-5500MkII
Digital: Yamaha CDR-HD1500 (Digital Swiss army knife-CD recorder, player, hard drive, DAC and ADC in one), PC files via 24/96 sound card and SPDIF, modded Philips CD850, modded Philips CD104, modded DPA Little Bit DAC. Sennheiser HD580 cans with Arkless Headphone amp.
Cables- free interconnects that come with CD players, mains leads from B&Q, dead kettles etc, extension leads from Tesco