The major difference is that 得 is informal and 需要 can be used in both formal and informal speech。 My copy of the 现代汉语规范词典 (a Chinese/Chinese dictionary) actually defines the meaning of 得 as 需要。Here they both mean “to need” or “to require.” 得 can also be used to indicate “should” as in “that should be sufficient" or "he should be worried” whereas 需要 does not have this meaning.

I think the answer above are all right,but I think there are some more diffierences.For example, I would say:我需要毛巾（I need towels, wo3xu1yao4mao2jin1) instead of : 我得毛巾（wo3dei3mao2jin1). Actually, I have never used " wo3dei3mao2jin1". But I would use both我得写作业（I need to do my homework,wo3dei3xie3zuo4ye4) and 我需要写作业(wo3xu1yao4xie3zuo4ye4). However, when I use xu3yao4 instead of dei3, I am usually much more determined. So, I think I will use both dei3 and xu1yao4 before a verb,but I will only use xu1yao4 before a noun.

Put it in a simple way,dei3 means "have to", xu1yao4 means "need"

Hi: The dei3 is a spoken Chinese word and is mostly used in the northern China area,it is roughly like the "gotta". the xu1yao4 is more formal and is like the "require".

dei3 -- should xu1yao4 -- need