I don't get all the people saying this season was worse than the first. That season started off moderately good with Index's arc (3.5/5) only to get somewhat worse in Himegami's actually pointless arc (3/5), later followed by the body-swapping arc which was nothing special (3+/5) and a nearly terrible four-episode arc to wrap it up about an overly trashy character I don't give half a fuck about, Kazakiri Hyouka (2.5--/5). Basically the only great things about that season were the Misaka/MISAKA's/Accelerator arc in the middle (4-/5) and the little two-ep installment introducing Last Order and developing Accelerator (4/5). Namely, seven episodes.
What about Season Two? I guess I'll make my point more easily by rating each of the arcs first:
Orsola Arc (1-5) -> 3.5-/5
Kuroko/Misaka Arc (6-7) -> 4/5
Daihasesai Arc (8-13) -> 3.5/5
Italy Arc (14-16) -> 3/5
Accelerator Arc (17-22) -> 4++/5
More Accelerator/Setting Up Arc (23-24) -> 3.5+/5
All around this was much more decent for me and the high points of the show lasted longer. Now, let's start by saying Index II shares many of the flaws Index already had, story-wise.
Big flaw #1: the sides of magic and science are barely in contact with each other except for Touma acting as a bridge. What I mean by this is that the show seems to deliberately avoid that the characters get involved in a world that's not properly theirs whereas this would start making everything much more interesting. Since almost all arcs about magicians have them sneaking into Academy City there's really no excuse to keep the resident espers and defense forces from kicking some ass. During many of these arcs I've seen so many wasted chances to get characters like Misaka or Kuroko into the fights with magicians that my head hurts.
Index seems stubbornly determined to divide its story in disconnected arcs concerning either of these sides. Season 3 hints at solving this problem somewhat, but given the path the series has chosen up until now I'm not getting extremely hopeful.
Big flaw #2: the way the anime presents the ''serious'' side of the story, particularly from the magicians' side. This is actually very related to my first point, but there's more to it. I guess it won't come off as a surprise for me to say this, but the exposition of the plot from which the arcs develop is deeply flawed.
The reason is that instead of getting the groups to act and fight in a more compelling way - that is, with major objectives, like a full-scale attack or the execution of a well-known character - we're being constantly introduced to some new magicians and a key person or people who are looking for some kind of strong, magically imbued artifact/spell to make their ulterior plans come to fruition. Be it a library of 103,000 forbidden grimoires, a vampire killer (wtf), a digital noise lump, the Book of the Law, the Stab Sword, the Cross of Saint Peter, the Queen of the Adriatic Sea or the goddamn makeup of Ronald McDonald. You name it. The thing is that the arcs mostly follow this basic structure, thus making them eventually dull and repetitive. It doesn't help to find Touma's constant preaching in every single one of them, as well as pointless enemy melodrama and so on so forth.
Now then, what has Index II done better? Well, for starters, a remarkable cohesion among the arcs can now be observed, albeit the show keeps lacking an unique, overarching storyline to unify all its elements. But it is an improvement nonetheless because I can finally see some proper connection for the stories. Secondly, the separate arcs, as standalones, are generally better. Characterisation is stronger (as well as interaction), comedy is better integrated, the intentions and members of the factions are more clearly stated and the fights are more plentiful and pleasant to watch. Characters like Index who were extremely passive and useless in the first season (funny fact for a titular character) get some chances to actively participate in the plot and even when their role is more passive their importance is considerably better noted.
Individually, the first arc works well as a reintroduction to the franchise: it includes the different churches, the usual conflicts for dominance, the already known characters from the magicians' side and a generous amount of slick action. The following mini-arc is different from the norm in its presentation and development and provides wonderful fights while reminding the most interesting plotline of the espers' side and keeping the cheesiness to a minimum. The third arc is pretty long and combines well the cute comedy with the serious business, but feels a bit drawn out at places and yet again fails to mix the characters from the two worlds in the same battlefield. The fourth is the least memorable arc and it could've easily been removed with not much being lost. The fifth is absolutely amazing and it gathers pretty much everything I love about the show, its shortcomings being - as always - the lame melodrama and preaching from the MC, but since the arc is all around so much more enjoyable these things are also easier to forgive. Finally the last two eps leave the path open to a promising third season that should easily outdo the former ones if only they play it out cleverly enough.
As in the original Index, the animation is simply gorgeous. With stylish character designs, detailed backgrounds, a careful use of shading and lights, fluid movements and flashy special effects, the show is just a treat to behold. The budget is clearly huge and it's been put to good use. No complaints at all here, really.
As for the soundtrack, I don't really walk away with much of an impression of it. Just like before, it has been used nicely to fit the respective scenes but beyond that it is easily forgettable. The opening themes are good enough but fall short compared to those of the first season. Voice acting is generally great, my personal favorite having to be the agressive, rash, troubled, severely twisted tone of Accelerator.
Characters are as always a mixed bag of sorts. There are great ones, okay ones, bearable ones and finally those who are pointless, useless or downright annoying. The good things about the second season regarding these are:
-Pointless characters like Himegami or Kazakiri get MUCH LESS screentime. Instead of dedicating whole arcs for their lackluster personas, their presence is almost anecdotal and I can't thank them enough for that as they now substract way less enjoyment from the experience.
-Characters I didn't really care about (or nearly disliked) in the first season, like Tsuchimikado or Kuroko, got more (and better used) airtime in this season, enabling them to augment their uh, ''likability'' and even develop. Tsuchimikado was little else than a pimp wannabe in my mind before but the arcs where he acted proved him totally different, and Kuroko mostly left aside her annoying ''Onee-sama'' antics to make good use of his teleport powers in fights and deliver some of the only non-cheesy lines/preaching in this series. Others like Styil didn't change my mind this much but also got significantly more watchable.
-Index is slightly less useless. Slightly.
-Touma, our archetypal male lead, keeps his hardly healthy mix of kickass fighter and dense preacher. While I deeply detest the second part, the guy has enough good points to make me unable to dislike him.
-Last but definitely not least, those who are for me the best characters by far got much more screentime and, again, more development. The sweet contrasts between Misaka's natural badassery and her extreme shyness/childish behavior are charming enough to make me melt, and I only regret she didn't get enough chances to fight during Index II. Accelerator is the show's major kickass without a shade of doubt and it's again the antithesis of his old sadistic vein and his present attachment/fatherly love towards Last Order that works so well in him (it's worth mentioning that any scene he's in seems 100x less cheesy than those of Touma). And then there's Last Order who is the embodiment of adorableness and one of the only (arguably) moe characters I can digest with pleasure.
Only shortcomings about characters in comparison with Season 1 are the outrageous passivity of Kanzaki in the plot and the fact there are still plenty of new uninteresting characters (like the Roman Church sisters) popping up everywhere.
Overall I just don't see how this season is inferior in any way to the first since it marks for me a big step from being merely ''good'' towards great, without quite getting there yet. The plot is somewhat more consistent, the individual arcs have also improved, there are more and better fights, the comedy/school slapstick aspect was much more enjoyable and the characters more likeable as a whole. Seriously, from where I stand I can safely say ''screw Index I for Index II is here to take the cake''.