Since
To know the difference one should know how deque is generally implemented. Memory is allocated in blocks of equal sizes, and they are chained together (as an array or possibly a vector).
So to find the nth element, you find the appropriate block then access the element within it. This is constant time, because it is always exactly 2 lookups, but that is still more than the vector.
vector also works well with APIs that want a contiguous buffer because they are either C APIs or are more versatile in being able to take a pointer and a length. (Thus you can have a vector underneath or a regular array and call the API from your memory block).
Where deque has its biggest advantages are:
The second of these is lesser known, but for very large collection sizes:
When I was dealing with large collections in the past and moved from a contiguous model to a block model, we were able to store about 5 times as large a collection before we ran out of memory in a 32-bit system. This is partly because, when re-allocating, it actually needed to store the old block as well as the new one before it copied the elements over.
Having said all this, you can get into trouble with std::deque on systems that use "optimistic" memory allocation. Whilst its attempts to request a large buffer size for a reallocation of a vector will probably get rejected at some point with a bad_alloc, the optimistic nature of the allocator is likely to always grant the request for the smaller buffer requested by a deque and that is likely to cause the operating system to kill a process to try to acquire some memory. Whichever one it picks might not be too pleasant.
The workarounds in such a case are either setting system-level flags to override optimistic allocation (not always feasible) or managing the memory somewhat more manually, e.g. using your own allocator that checks for memory usage or similar. Obviously not ideal. (Which may answer your question as to prefer vector...)