Alot of times the bg instruments are based on the original song's bg. Usually, though, they remix a song just to remix the song, and then make a dub version for people who like the new arrangement but aren't fond of the original song or the vocals to begin with. Sometimes you end up with a composition that's really amazing, like kanariya's dub version by hex hector.
EDIT:
Here's ayu-mi-x 1... Some of these took research
~ Alot might be wrong, if anyone out there knows more about EDM than me, feel free to correct. ^^
1. poker face (Spiritual Guidance Mix) - Dream House
2. Hana (D-Z Deadly Rose Approach) - Big Beat
3. SIGNAL (Y&Co. Taste) - House
4. Depend on you (Dub's Electro Remix) - Dream Trance
5. FRIEND II (Make My Mad Mix) - Big Beat Industrial
6. Hana (Dub's Trance Remix) - Trance
7. Powder Snow (Dub's Sentimental Remix) - Balearic
8. Trust (Groove that Soul Mix) - Deep House
9. Signal (Groove that Soul Mix) - Funky House
10. As If... (DJ Turbo Wish Mix) - Funky House
11. You (Masters of Funk R&B Remix) - R&B
12. From Your Letter (DJ Hasebe Remix) - Acid Jazz?
13. Two of Us (Rub Delight mix) - Trip-Hop
14. A Song for XX (Dub's Loverdub remix) - Dub
Here's ayu-mi-x II US+EU
1. Boys & Girls “Main Radio mix” - Progressive House
2. too late “Soul Solution remix” - Tech House
3. appears “Junior’s Appears On The Air” - House
4. monochrome “Orb 7″ Vocal mix” - Chillout
5. End roll “Mumu Dub mix” - Big Beat
6. Fly high “SAMPLE MADNESS remix II” - Breakbeat
7. And then “Rhythm Masters Vocal 7″ mix” - Pumpin' House
8. WHATEVER “Ferry ‘System F’ Corsten Vocal Edit mix” - Progressive Trance
9. Fly high “Vincent De Moor Remix Radio Edit” - Pop Trance
10. Boys & Girls “Junior’s Radio Version” - Tribal House
11. Trauma “Thunderpuss remix” - House
12. kanariya “Main Radio mix” - Progressive House
13. Who… “Who Dub It?” - Dub
ayu-mi-x II version JPN
1. Trauma "Yukihiro Fukutomi Remix" - Italo Disco
2. Fly high "Groove That Speed Mix" - House
3. immature "Club Bahia Mix" - Latin House?
4. too late "Lab Life Remix" - Bitpop
5. Boys & Girls "Inskadisco mix" - Synth Ska
6. WHATEVER "FPM's Winter Bossa" - Shibuya-kei House
7. End roll "Da Urban Maestro Mix" - Drum & Bass
8. Who... "Blue Obsession Mix" - Ambient/Balearic/Chillout
9. And then "Future Disc Mix" - Hard House
10. monochrome "D-Z White Instinct Mix" - Big Beat
11. appears "DJ-TURBO Remix" - Italo House
12. P.S II "Dub's Kingship Remix" - Dream House
I'll do more later... i'm tired. XD