Just to throw in my 2 cents ...
For me the question of swap file vs. swap partition is largely a matter of convenience. Lets say 10+ years ago I spend quite some time and effort in trying to find the "perfect balance" by creating a lot of different partitions for several Windows (98 + NT, later replaced by 2000) and Linux (e.g. SuSE) installations on a single 30 GB disk. It took a while and in hind sight I never got it right. Sure, all the different OS were booting, but somehow I always ran out of space in one file system and had maybe too much in another one. The swap partition for the Linux system was at one stage deemed particular "wasteful". In the end I've come to the conclusion that I tried to be too clever for my own good.
Nowadays I'd always prefer to use a swap file as I could put it on pretty much any file system (e.g. EXT[2-4], or even VFAT or NTFS) and (provided the file system it resides on is mounted) the swap file could become my swap space. No need to engage in re-partitioning to adjust sizes. If I need more swap space I can easily create a larger swap file, and if the file system it is currently on does not have the required additional space I might be able to shift it to somewhere else.
So, if you already have a swap partition and you are happy with it's size then by all means use it for TC. OTOH I for one would not want to create such a partition any more as I'd rather have only a minimal number of (larger) partitions on my disks.