Everything
Firstly their history... Quenya is the language of those that live in the Blessed Realm, Sindarin is the tongue of the others who stayed behind in fear at the shores of the great sea, of those that call themselves the Lost People, of those that live in the dark woods instead of libraries
though it later became the language of nearly all elves in Middle-earth
That's also what they sound like - Sindarin like something growing, living, fearing, Quenya like cold letters scratched with a quill into the pages of a book
.. ok that was a little exaggerated
but quenya sounds more sophisticated
The actual phonological differences:
- Quenya uses semivocalic 'Y' as a consonant, Sindarin as a vowel; ie when in a text there's a word like 'thynd' with a 'y' between two consonants, it's Sindarin as the 'y' then can only be a vowel while when you have a word like 'yanta' where the y is obviously consonantic itself it's Quenya... typical for Quenya are also combinations like ny/ty/ry/ly+vowel.
- 'qu' and derivated combinations like '-ñqu-' or 'Ñgw-' do not exist in Sindarin; neither do hl, hr or hy+vowel.
Instead, combinations like dh, ch, lh or rh are pretty frequent in Sindarin; those are not allowed in Quenya.
- most words in Sindarin end with consonants hence the usage of diacritic vowel signs on the following consonants in Sindarin-Tengwar instead of the preceding like in the Quenya mode]; in Quenya, words end mainly with vowels, the only final consonants allowed are N, L, R, T and S (> those from the tincotéma and liquids). Most writers use '-ë' to mark that the final 'e's are pronounced, so 'ë' is also quite typical for Quenya texts, though that isn't directly because of the language.
- in Quenya, d, b and g only occur in the middle of words after the corresponding nasal (n+d, m+b, ñ+g) or the liquids r and l; in Sindarin, they usually stand alone and also occur initially or finally;
The voiced spirant dh (=ð) doesn't exist in Quenya hence the usage of the third and fourth row of the Tengwar table for combinations with nasals like nt, nd, mb etc in Quendyan mode instead of - like in Sindarin - for voiced sounds like d, g, dh etc]
- long vowels are marked with a circumflex in Sindarin (â, ô, î etc), but acute-accents (á, ó,...) also occur, usually in polysyllabic words; in Quenya, only the acute (and sometimes diëresis, like on ë) exists. A middle point, a - or a ' is often used in Sindarin to mark a following sound mutation (like in Tuor's famous quote 'Alae, (...) ered e-mbar nín', -mbar being mutated from 'bar')
- Quenya uses ai, au, oi, ui, iu and eu as diphtongs, Sindarin has ae/oe (and others, but those also exist in Quenya)
- w is rather rare in Quenya and usually just the alternative writing for v; x exists, but only in few words (for example 'Helcaraxë'); 'th' only occurs in old Quenya (used in Aman), after a phonetic revolution, it changed to 's' (hence the name of the letter 'thúlë' changed to 'súlë') and only few, like Fëanor, still used the old 'th'. 'Z' sometimes occures in old words instead of 'r' and in some names ('Ezellohar', imported from Valarin).
In Sindarin, w and th are quite frequent, but x and z do not exist.
The grammar is of course pretty different in the two languages; the most obvious thing is that Quenya-words are usually a lot longer than Sindarin ones (just look at the names from the Silmarillion - 'Noldolantë', 'Valaraukar' or also 'Silmarillion' itself, that's Quenya; names like 'Iant Iaur', 'Ladros', 'Laer Cú Beleg', 'Lammoth', 'Balrog' (=qu. 'valaraukar'
) are Sindarin; the word 'Sindarin' itself is also a Quenya name *laugh*)
This is mainly because Quenya works with a lot with suffixes while Sindarin is using prepositions instead. There are 10 cases in Quenya, all constructed with different suffixes and also used to express things like directions ('Elenna', a name of Númenor, for example, is the allative of 'elen' and means 'to the star'; in Sindarin, this would rather be 'nan êl' or so, 'na' being the preposition); same for possessive pronouns
Quenya verbs also often include loads of suffixes to express all the different pronouns, for example 'laituvalmet' ('we will praise them') is composed of lait- 'praise', -uva- , -lme- 'we', -t 'them'; in Sindarin, objective pronouns are seperated from the verb ('Le milin' - 'I-love you', the Quenya form would be 'melinyet')
One of the essential elements of Sindarin grammar are sound mutations, of vowels for the plural forming and of consonants in initial position; the results sometimes look a little funny to 'english' eyes (words like 'i mrýg', ' i chloer' or 'or dhring' look kinda strange...) and are not always easy to recognize, like
i 'aladh 'the tree', plural i-ngelaidh 'the trees'
All in all the two languages have totally different characters and when you for example compare some quotes from LoTR, you will easily be able to tell which is Sindarin and which Quenya, even if you don't understand a single word of it
and way too proud, kinda unnatural, why Sindarin sounds like the growth of trees or the waters of a small well 
I sometimes talk a few words to my friends in Sindarin, but hardly more than greeting and asking how they are 
animals 
). thats why i think feanor is evil.