My Droid mini have a strange problem, when I am charging the phone with some USB cables it charges very slowly and phone battery discharging very fast. but when I charge with original cable it works normal. are there any differences between the usb cable quality? thanks
Yes, this is well possible.
Ususally, the manufacturer advises to use its cables only. But usually, there's no problem with other cables.
However, there might be a problem with the phases of the cable. Sometimes if a cable is folded one or more of the phases can break or a solder joint at the jack might be loose.
If it's the wrong one, your phone might charge very slow or even not at all.
But you also mention that your battery drains fast.
You can take a look at it by using apps like Better Battery Stats by chamonix or the usual battery monitor.
If you don't find any strange energy-consuming threads, then it might well be the cable - either a defect like broken phase.