I believe Peggy has a good point. And in my opinion, these two sentences has no difference in daily use. It depends on yourself which one to use.

The difference is in the implication of the English translation. 你要呆多久？ How long are you going to idle away? 你要呆多长时间？How many long hours are you going to idle away.

There is no difference between these two statements in this sentence, but for "久" and "长时间", there will be some differences in the following sentences: 好久不见！（More formal, it often appears in letters） 好长时间不见了！（More colloquial, which is often said in daily life）

The two sentences mean the same

There's no difference.