The word "wciąż" implies "persevere" whereas "jeszcze" implies only "still".
I'd say that 'wciąż' just adds some emotions to your expression, while 'jeszcze' only indicates the 'timing'. E.g.:
Wciąż ci cię chce tu pracować?
Do you still want to work here? (even though nobody else wants...)
Tyle razy ci to mówiłem, a ty wciąż nie pamiętasz!
I told you it so many times, but you still don't remember!
'Wciąż' also may mean 'always' e.g.:
Wciąż ci powtarzam, nie pij tyle!
I always tell you, dont' drink so much!
you shoudl also know that wciąż = ciągle e.g.:
Ciągle pada i pada...
It's still raining and raining...
Cinek
