Comparing open reed and closed reed, in my N=1 experience is really a discussion about distress calls. When it comes to howlers, open reeds are the only game worth playing (bite reeds maybe, but they're not in your discussion).
So discussing distress calls...
Closed reed is bread and butter, straight forward, easy to play, easy to learn. Limited on pitch it can produce, so it can only be used to make one sound, or a few sounds at best (some closed reed cottontails can be made to cluck like a chicken pretty well). The caveat I'd offer is that closed reed howlers are out there, and none of them work very well (MAD Cherry, Knight & Hale EZ Howler, Buck Gardner 2Fur), so again, howlers are a different discussion.
Open reed is far more versatile, but takes a bit more skill, therefore has a longer learning curve. Callers can slide up and down the reed, changing the natural resonating frequency of the reed and giving the caller control over the pitch. This means one reed/toneboard can be used to play a number of different sounds.
What you use will ultimately be personal preference. Some guys like the simplicity and "bubba-proof" nature of closed reed calls, some guys worry about reeds freezing or want more versatility in their lanyard, so they use open reed calls.
So open reeds have the advantage of versatility, closed reeds have the advantage of simplicity.