In a nutshell, avoir besoin is about needing (or needing to do) something while devoir is about having to do something.

avoir besoin de qqc -- to need something
avoir besoin de faire qqc -- to need to do something
devoir faire qqc. -- to have to do something

Je dois aller au banque. -- I have to (=must) go to the bank.
J'ai besoin d'aller au banque. -- I need to go to the bank.

The question related to the usage of ‘devoir’ and ‘avoir besoin de’, not avoir envie de. Chris’s answer marked correct, is not wrong, but not the answer to this question. 

‘Devoir-infinitive’ (eg faire) is ‘have to (do)’ - relates to obligation, and in conditional present tense, should (do). It does not mean ‘have need of, or wanting’  something. ‘To have need of something’ is ‘avoir besoin de qqc’. Unlike ‘devoir’, ‘avoir besoin de’ can be followed by infinitive or noun, and mean ‘need (to do)’ or ‘need (something)’.

‘Devoir-noun’ changes the meaning of devoir,  and means ‘to owe (noun)’. Explained in attached lesson: 

Devoir vs Avoir besoin de to express "to need to" in French

Hi Maarten, thanks for pointing this out. Must have been on autopilot. I adapted my response accordingly.