Let's start with the basics. Alliteration is supposed to focus readers' attention and create rhythm and mood. A really useful device, especially if you are feeling poetic or descriptive but not so much in a legal document or bank correspondence. 'Dear Dr Beaver your actual active account is disastrously dour and dipping down into the depths of doom. Please calculate carefully and debit dosh.' I am not impressed. As with all language you have to know your audience.
So if alliteration is the repetition of the same initial sound, not necessarily letter, at the beginning of adjacent or closely connected words, then what is sibilance? The simple answer is that sibilance is alliteration. However, it is more sinister than that. Sneaky sibilance is sleek and smooth, it relies on the repetition of the fearless fricatives: ts, dz.s..sh & zh. It often creates a negative tone, unless of course you are fond of evil and slimy slippery serpents.
Although alliteration can be provided by either vowel or consonant sounds, sibilance and consonance only include the recurrence of similar-sounding consonants. The difference here is that sibilance like alliteration is only at the start of words where consonance can be at the beginning or middle of the words but is more typically found at the end. Again with consonance you have to remember that it is all about sounds and not necessarily letters,
for example, the obvious 'cheer for beer' which less obviously makes some people 'laugh and barf'. You can tell what I have been listening to on the news this weekend!
I think that consonance often just happens and is not crafted by many, a little like assonance really which is the repetition of vowel sounds within words, 'count sheep and sleep'. That is how boring I find it but I would imagine that poets ponder such points persistently. I am happy to stick with simple alliteration and on a bad day sibilance.