By safer I mean limiting the chances of conflict. For example, even the basic k-lite codec pack as redundant things in it. It has a MP4 and FLV splitter in addition to haali, but haali already can handle these two formats. It also have directvobsub for subtitles which ffdshow can handle perfectly fine on his own.
And if you take a bigger pack, in addition to the redundant codecs like xvid and divx starting in k-lite full, it will also include codecs for encoding and additional tools to tweak which most people don't even know how to use or will never touch.
Also, there is a big chance that people will take the most complete pack, because they think they will have less problems since it includes so much that it will be able to handle anything.
In most cases, it won't cause any problems, but there are always exceptions and in those times, I always fixed it by removing unnecessary things from codec packs.
If you encounter a video that doesn't work with only ffdshow, there are tools to easily identify the missing codec(like AFREECODEC VT mentionned by slimedog) and a simple google search will tell you where to get it if the software doesn't. But in my experience, I rarely need to install other codecs nowadays. For example the only other one I have installed are: coreavc(because my cpu is not fast enough to use ffdshow for h.264), corevorbis(from 2005, because I use spdif on my old onboard soundcard and in all the vorbis codec I found it's the most compatible with my 5.1 decoder), QTlite and realAlternative(because I always did, but I'm not even sure if I really need them since ffdshow has support for both of them)
But, if I had to choose a codec pack, it would be cccp since it has the least unnecessary things (in my opinion). The only thing I have against it is that it's not enough up-to-date with it's content for my taste and I personally like to have more control over what I'm installing.
This conclude this way too long post of mine. Let us know if you ever find your problem lcchan.
Edit: BTW wwilk, there are 6 different version of k-lite and the only(useful) difference in playback between standard and basic is an additional codec for DVD playback.