Having owned and carried snubby J-frames, K-frames and a Detective Special, I'l throw in my two cents.
I much prefer the DS to the J-frames. The little Smiths are just too little for me to shoot well. The DS, OTOH is an excellent size for CCW while still being big enough to shoot quite well. I carred a DS for several years and was never the least bit uncomfortable with it.
When compared to a snubby K-frame, its strictly a matter of taste. The Ks are a bit larger and heavier, but not enough to be of any real concern. With a good holster, I find both suit me very well. YMMV.
The advantage of caliber goes to the Smiths, which can be had in .357 Magnum. In my case normally, for a snubby .38 I go with the detective Special. If I should decide to go .357, then its a snubby Smith.
Should you decide to go Colt, there are some things you need to know in regard to the snubby D-Frame family. There have been three versions of the Detective Special. First Issue (pre- WWII), second issue (post WWII) and third issue (1973-86 which had the shrouded ejector rod). First and second issue guns are now pretty much collectors items. Third issue guns are the ones much sought after as carry pieces. Also in this family are the Cobra (lightweight) and Commando (parkerized) models.
All of these guns are out of production with the last ones being made in 1986. As a result, snubby D-frame Colts can get very expensive with good examples running in the $500 range.
There was a short lived Fourth Issue version of the DS in 1993 to 95. However, it has been reported that they failed due to poor quality control.
In 1995, Colt completely re-engineered the D-frames resulting in the SF-VI, DS II and Magnum Carry. While they are the same size as the old Detective Special, internally they are completely different guns. IMHO, none of these is anywhere near as good as the eariler DS and I wouldn't have one of them. In short, they were junk. It should be noted that none survived very long on the market. SF-VI (95-96), DS II (97-98) and Magnum Carry (1999 only).
To recap: If money is an issue, The Smiths are definately the way to go. They are plentiful, easy to find and considerably cheaper.
However, if you do find a nice original Detective Special and don't mind the premium price, I can promise you that you'll never regret buying it.
JMHO