Translation:Is there a lot of luggage?
I don't know if this information is correct, but I find this link pretty useful:
I personally find the 2 to be interchangeable in meaning, but the way to use them is different. Consider the following.
おおい seems to act as a い-adjective while たくさん is weird in that it needs to be connected to some other word, whether it be to a noun or to a verb. It can even be attatched to a adjective or some other descriptor word when おおい conjugated can't to provide the same meaning.
In this example, おおく feels off as it has more of "most" kind of feel rather than "a lot" and would be more like ほとんど in meaning and use...