何百というふくろう is very close to 何百ものふくろう:
- 数百(羽)のふくろう
several hundred owls
- 何百(羽)ものふくろう
hundreds of owls
- 何百(羽)というふくろう
hundreds of owls
Although the latter two are translated into English the same way, I think the という version is a little more emphatic and literary, and often has a stronger connotation of "countless". I think it's best to remember this as a common grammar pattern rather than asking why. (Grammatically, 何百という is a relative clause that modifies ふくろう, so a super-literal translation is "owls to which one says hundreds".)
You can say the same thing adverbially:
- ふくろうが数百(羽)飛び交っている。
Several hundred owls are flying about.
- ふくろうが何百(羽)も飛び交っている。
Hundreds of owls are flying about.
In this pattern, 何 must be used with も, so 何百のふくろう and ふくろうが何百飛び交う are both ungrammatical. (You can say 何百のふくろう if you are asking "how many hundreds of owls?", though.)
EDIT: An important difference from ~もの is that you can use という only with 何. For example, you can say 83羽ものふくろう ("as many as eighty three owls") but not 83羽というふくろう.