Yes FAT32 has a file allocation table. basicly the same thing as MFT.
The FAT (Table in the acronym is a bad choice because it's not really a table) is a huge list of all the files and their place on the disk, every time you open a file the driver has to search the entire list linearly so on big disks that search can take a very long time (in computer time). And all it holds is filenames and the first cluster, you have to navigate the cluster chain to find an arbitrary place in the file and the files info. And LFNs are a big hack, they use another cluster to hold the filename because FAT doesn't leave any room in the "table" for filenames over 8.3 length, so just using LFNs loses you some disk space.
The MFT in NTFS is a real table that holds a lot more than the filename and position on disk, and if the file is small enough it gets put in the MFT for faster access.
NTFS is just a better designed filesystem, you should be asking why you would want to use FAT32 over it, not vice versa.