The two modules share a lot of features, and at there are many tasks which can in principle be tackled using either. To understand the reason for the existence of both, I'll first highlight what seq can do that clist cannot.
A comma-separated list looks something like
a,b,c,d,,
which means that most obviously the items cannot contain a comma (without brace protection). On the other hand, the seq data type is constructed such that an item may contain any balanced text. That includes not only commas, but also crucially empty entries.
The latter point occurs because a comma list is essentially a 'user facing' structure, whereas a sequence is meant for programmers. You'll also see this if you try adding a space to a comma list: spaces are trimmed from comma list items, and so something like
a, b , , c , d
is treated identically to
a,b,c,d
As sequences have an internal structure to support programmers, it's also possible to optimise the implementation rather more than it is for comma lists. That has consequences for performance in some cases.
So in terms of which is appropriate, I would favour comma lists when dealing with stuff toward the user level, for example where user input/output is required. On the other hand, totally arbitrary lists of items are better handled as sequences. There is an element of personal preference in the middle ground (where both will work).
In the past, I have suggested dropping clist functions entirely except for a conversion layer (so that we would have a single 'true way'). However, if cases where basically everything can be handled using a comma list there is a performance hit to this that is hard to justify.