With a lvl 50 Sniper and a lvl 26 Assassin, my opinion may be quite heavily biased towards Snipers... but here's my personal experience with both (also note, my Assassin is Tank, or Darkness spec)
PVE - which class is in higher demand, and does better damage?
demand, I'm not sure, as Tanks are generally more in demand, and Assassins can tank, I'd say Assassins... better damage, obviously as my Assassin is a Tank and not DPS... Sniper...
FUN - Which class is funner, and has a more complex (not too complex!) rotation
Snipers CAN be complex... their cover mechanism takes some getting used to, and some outright hate it, but personally I love it... rotation can be very flexible depending on the situation, and it really takes practice to get some of the right... as I always forget I had certain skills that I only realize I could've used before the fight ended...
As an assassin, since I'm still not too far, and still have a bad habit of playing a Sniper for longer, I can't say I'm any good at it... but I'm still having fun at being able to jump into the middle of a mob and just tank... without worrying about being overrun XD
levelling - which class is easier and funner to level?
this is EXTREMELY biased, as my Sniper's lvl 50... this HAS to be Sniper... for 2 reasons... 1: see the next part, 2: it's lvl 50... I've been through the story and all the planets already... on my Assassin, I'm basically just repeating some of the parts
Storyline - Which class has a better storyline?
I've been hooked on the Agent story since the beginning... great voice acting too! (female agent)
however, I love all the sarcasm from the Inquisitors, and they're quite hilarious sometimes, and is SO MUCH better than the Consular counterpart imho... but overall I think I prefer Agent story but so far, Consular's not so bad... (at least compared to smuggler, which I haven't gotten over lvl 7 yet >.> maybe being the first toon I made and having been completely lost on story, mechanic, what to do in general didn't help... might make a new one in the future)
overall, I prefer Imperial stories vs the Republic ones...
PVP - (not that important) which class plays better in warzones?
only PvP'ed on my Sniper till 49, and about 3 matches at 50 to get the battlemaster rifle... not touched since... but I think Snipers, if played right, can be quite good... never tried PvP with my Assassin yet, so I can't really tell... but being a tank, I think it plays completely differently
Companions - Which class has the best companions/storylines/romances? (advice on which companion to use while levelling is useful too)
Sniper, you're stuck with Kaliyo for a LOOONG TIME until you finish Alderaan, where you get Vector (only romanceable companion for female agent) and then doc on Taris... then Temple on Hoth and SCORPIO on Belsavis... they each have their own unique and interesting personalities which make them quite awesome (maxed affection on 4/5 of them... only SCORPIO left) then there's the new HK-51, who's quite awesome in his own regard! XD
Assassin, only Khem Val so far... and since I'm tank already, I don't need him much... which is where HK-51 comes in XD just got to Tatooine and met Andronikos but haven't gotten him yet... so can't comment on further companions yet...