The answer all depends on your definition of "efficient." Do you mean which performs faster or which consumes the least disk space and memory for a given partition size?
Let's start with disk space and memory. A file system makes the most efficient use of a disk by having the smallest cluster size. This minimizes the wasted space at the end of each file.
NTFS is a 64-bit file system, so it can support many more clusters than FAT32. This means each cluster can be smaller, making more efficient use of the partition. It's possible with NTFS to format a 300GB partition with 512-byte clusters. This isn't advisable, though, because the file system would need to contend with many more LCNs (Logical Cluster Numbers), which would slow it down and consume more memory.
NTFS is a true database, not a cluster map, so it takes up more room on disk and in memory than FAT32 for small partitions. NTFS would consume 7-10M bytes of a 50M byte partition if it holds lots of files and directories. But in today's computing environment, 50M bytes is scarcely a functional partition. Heck, it's barely enough for a Word document header. For realistic partition sizes of 2G bytes or more, NTFS will consume less disk space and memory than FAT32.
As far as performance, FAT32 can outperform NTFS on small partitions as long as you defragment frequently. (By small, I mean 500M bytes or less.) The FASTFAT driver in Windows 2000/NT keeps the FAT32 cluster map in memory. This improves raw lookup times. But many applications, especially databases, don't just open a file and read the whole thing. They do random access to a particular byte to find a record. NTFS performs this kind of random access more efficiently. And NTFS resists the effects of fragmentation much better than FAT32. Sure, you have to defrag an NTFS partition every once in a while, but nothing like you would need to do with a FAT32 partition.
So, for small partitions and light file loads you might get marginally better performance out of FAT32. In production, though, the performance improvement is far outweighed by the stability of NTFS.
Based on raw speed numbers, FAT32 probably has the performance edge. See this comparison of two high-performance drives formatted with NTFS and FAT32: http://www.gamepc.com/reviews/hardware_review.asp?review=fireballlm&page=1
This was first published in February 2001