Can't speak to changes since 7th since I played from late RT to the very earliest part of 5th - and mostly played 4th - until returning in 8th, but as to specific questions:
My question is this. As a competitve* strategy game how has the game changed since 7th? specifically how do the eldar play since 7th and their new codex release.
I like the way they play a lot - they feel a lot more 'Eldar' with the Codex than with the Index rules, with their mobility and firepower somewhat restored and the best non-special character psychic powers in the game. Having said that I have not been having a great deal of success.
In large part that's because of significant play choices rather than the usual 40k issue of 'who rolls best, wins', which is welcome. The downside is that some of those play choices are a case of not being aware how to game the rules (such as the 'multiple charge' system and need to keep units widely separated from one another to avoid getting them caught in combat unable to fire when they neither charge nor were charged and yes issues being unfamiliar with specific auras), rather than truly tactical decisions.
Oddly, given that the ruleset is essentially identical to Age of Sigmar which is (presumably) a close-range game, the assault and melee rules are especially poorly thought-through and open to unnecessary exploits (such as charging past an intervening unit with the ridiculous notion that a solitary model can simultaneously charge two units, and completely bypass the first - negating a whole area of tactical positioning to keep ranged units from harm present in earlier games).
my take so far is that the game seems to revolve around getting a big buble augment effect(s) and then capitalizing on them.
That's more significant for some armies than others (I lost a game today in large part because of the Shadowseer aura nullifying most of my attacks), but in fairness this has always been the case to a large degree.
Overall I'd say the most important aspect of the game - and the one where it's a big improvement over the versions I used to play - is correct use of command points and stratagems. You can basically think of 40k8 as a bad (and in a couple of areas terrible) core ruleset with an excellent tactics card system, rather than as a good game in its own right. Now that the Codices have nearly all been released the game plays much better than it did at release.
Is terrain important? how important?
Broadly I'd say not particularly as far as defence vs. shooting (it now does nothing at all in assault), but then I play on relatively terrain-light boards (and with a mobile army that can obviously often avoid directional cover protecting enemies). It can be very effective at blocking LOS, though, as mentioned above. Terrain works very strangely in 40k8, in that it provides a save modifier rather than a to hit modifier. With the reinstatement of save modifiers, 40k8 has many of the problems that led to the system being removed in the first place: modifiers often make armour irrelevant, and the +1 from cover is therefore relatively marginal.
The corollary is that now invulnerable saves are absolutely everywhere, and frequently set at 4+ and above, which makes it much less punishing to simply stand about in the open than it otherwise would be. Remember how the change to the AP system in 40k3 meant that Marines didn't care in the slightest about cover since they ignored AP4 and 5 weapons that were the norm? Transpose that to basically every army that isn't Guard, Tau or (non-Harlequin) Eldar, and that's 40k8. Oh, and basically every army is also swimming in ways to give saves (usually 6+) against anything that bypasses armour anyway.
where are the big tactical choices in the game?
How to use command points and what to target when shooting. That's basically it - so, a whole system (command points) more than 40k has offered in the past. 40k8 is not a game for especially serious tactical wargamers - but it's 40k, a game which never has been. Warhammer 40,000: standing across the board from the other guy and rolling dice at each other until someone's dead since 1987 (except 3rd Edition, where it was all about charging and rolling dice in melee until someone's dead).
what do competitive lists look like? for eldar?
What do competitive lists for Eldar look like? Dark.
for others? what does competitve play look like (in general obviously)?
Knights and Imperial Soup, apparently. In 40k8 there are no longer major and subfactions - in place of 9 major armies with specific, essentially mutually exclusive subfactions like Marine Chapters, there are now upwards of 20, and rather minimal restrictions on how they can be mixed and matched. Basically anything belonging to the same race can ally with anyone else. So, for Eldar, for instance, it seems optimal lists are essentially Dark Eldar with attendant Dark Reapers and possibly Wave Serpents.
This is a fundamental mistake - word is that a fix may be incoming for the Imperial issue specifically, but the problem is with the concept and GW feels that people like mixing their factions together too much for them to be likely to ditch the system, as would be ideal.
How has the change to AP, damage, and to hit rules changed meta list building?
I don't know what the 7th Ed. meta was, but a change in the current beta rules - which will probably be official in the next Chapter Approved - restricts the number of units of a given type (to a maximum of 2 in typical tournament-style armies). Given 40k's tournament scene's infamous tendency towards 8 Dreadnought or all-Razorwing Flock armies (the latter not a thing in 4th but I've heard about it), this is likely the most significant overall change in years.
Probably one of the bigger changes is the removal of AV.
I neglected this, but indeed it's huge - and probably especially for Eldar. The short of it is, Eldar are now far worse against tanks than they used to be. We still have very high-strength weapons, but these nearly all have damage 1 or (low) variable damage output - where before you could reliably take down a tank with a small number of fusion guns or heavier anti-tank weapons, in a world where main battle tanks have 14 wounds and prism cannon only deal D6 (same as a lascannon) at most per shot, most Eldar AT platforms are inefficiently priced relative to other races'. The new damage table is also not kind to the Eldar arsenal of S8-10 weaponry, as S10 wounds on the same rolls as S8 against most things (with 6-7 being the common toughness values for most tanks).
The new system does allow Eldar AP weaponry to do damage to vehicles, as low strength weapons with large numbers of shots, like lasblasters, can actually harm them in principle - and more importantly, with no distinction in the base rules between infantry and vehicles the assorted 'free' ways Eldar have to cause mortal wounds (psychic powers, Ranger longrifles, Hawk grenade packs, mandiblasters...) are all strong against vehicles. Which results in the oddity that Rangers can actually be anti-tank units.