I've played a bunch more games with the first two starter decks of Diva (Ancient Suprise and Nijisanji), and I've also gotten a few games in with No Limit, the third Diva precon (and I've looked over the next 3 preconstructed decks for the Diva format - which are currently awaiting sleeves). Like the transition from original to Key format, I've had to re-evaluate several assumptions I have about how to play these decks. I'm pretty confident with these decks now, so I figured I'd share a few of the biggest things to watch out for, either playing these decks as a new player, or as a returning player used to the decks of the Key era.
Ener management
Ener management played a heavy role in early Wixoss. Carelessly attacking would often just give your opponent the resources to hit you back harder, while attacking opposing SIGNI as little as possible could help starve your opponent of ener and leave them with nothing left to defend themselves after paying a hefty 3 ener to grow to level 4. Key format introduced two big changes that significantly reduced the pressure on ener - coins and 0-grow-cost level 4 LRIGs. Coins were a parallel resource that could often be used in place of ener - several Arts used Coins to reduce their ener costs, and Keys traded coins for powerful effects without any ener requirements at all. And with 0 grow cost, players entered level 4 with a much more robust stock of ener to immediately spend on offense or defense - you no longer had to spend a turn or two rebuilding after your final grow. Later Key decks started to reintroduce incentives for canny ener management, especially with powerful 6-cost Arts that could be game-breaking if you managed to generate enough ener to use them after covering all your other costs (Bloody Strike and friends). But these decks still generally performed at a high level with relatively meager ener budgets.
With Diva, ener management is back in a big way. While in Key there were often turns you didn't need to enercharge at all, you should be using your one enercharge at the start of the turn every turn of the game in Diva. There are several reasons for this, all attacking your ener supply at once. First, we're not really shaving costs anywhere; level 4 LRIGs cost no ener, and Assists total to about the same average cost we're used to with Arts (although more divided - level 1s are usually free and level 2s can be quite expensive). Second, there are a lot more ener sinks - in the main deck and also with Pieces. And while the cost-to-return rate on Pieces isn't great, they're still powerful effects you'll want to be able to access; they can usually push 2 damage or more while building card advantage. As for the main deck ener sinks, all decks seem to have offensive SIGNI that require 2-3 ener to clear a lane (Otogibara Era, Atalanta, Adamasphere), and both have other tools for defense that require ener as well (Otogibara Era again, Polygenesis for a Servant, etc). Figuring out when to spend your ener, and where, are very, very important to maximizing the power of your Diva precon decks.
Of the first three preconstructed decks of Diva format, No Limit is the least stressful as it's costs are quite low across the board (most importantly, the Piece costs 0). However, the deck is also less stressful for your opponent as well, due to the deck's mass of banishing effects which will give your opponent a steady supply of ener to draw from. Ancient Surprise has a lot of costly effects, but generally has the tools to keep up with them - it has several solid enercharge effects (At level 3, Tawil-Colors, and Sen no Rikyu's life burst), and can still operate a solid game plan with less ener resources due to the low grow costs of its Assist LRIGs. Nijisanji struggles quite a bit more, as not only does it lack enercharge effects (including in life bursts) and has more expensive Assist LRIGs, but the deck's core game plan centers around Era, and she is HUNGRY. She does a lot: returning guards for defense, clearing lanes for attacks, or both, and the deck can easily play out an Era each turn (no matter the configuration, this deck has tons of trash recursion). But with few effective ways of generating ener, being able to use her while using your Assist LRIGs and Piece is a struggle that requires a lot of reading of game states. Do you want to use her offensive ability, her defensive ability, both abilities, or do you want to use your ener on an Assist LRIG or Piece instead? It's heavily context dependent, and you'll rarely be able to do more than one or two of these in a given turn.
Card Advantage
If ener is in short supply, the opposite is true for card draw. There are tons of ways of adding cards to your hand, to the extent that even after enercharging every turn of the game I'll still have turns where I discard to hand size. In Ancient Surprise there is Umr-Draw, Tawil Colors, and the Piece Harmony Call that all generate cards in hand or SIGNI on the board. With Nijisanji, there are the level 3 LRIG effects, several Assist LRIGs (Lize level 1 and 2, and Toko level 1), as well as SIGNI effects from Morinaka Kazaki and Otogibara Era. And in No Limit you have Rei level 1 and 2, as well as Tlet. Since cards in hand are much more plentiful then ener, this makes it all the more important to deny your opponent ener by only attacking when you're guaranteed damage. As a side effect of having plenty of card draw available from level 1 (at least one of your level 1 Assist LRIGs will draw cards), you should make sure you deploy two level 1 SIGNI on your first turn. In older decks you could occasionally get unlucky and draw 1 or even 0 level 1 SIGNI in your starting hand and have to deal with taking an additional point of damage during the opponent's first attack, but in Diva the limited attack-phase interaction makes falling behind early even more painful. Using an early Assist LRIG to help you fill in your field at level 1 won't hurt you later in the game, given the number of ways to generate cards in these decks.
Servants
Since the start of the game, we've been used to having 8 servants in our precons, and up to 12 options to play around with during deck customization. Diva only has one Servant so far. Fortunately, all three decks have ways to get more uses out of their limited servants, and I've still had plenty of games where LRIG attacks only manage to deal 1-2 damage over the course of the entire game. Ancient Surprise can pull the Servants from ener with Polygenesis, which turns enercharging into a kind of card draw, and also lets you use Servants that ended up in your life cloth. Nijisanji has Era, and tons of ways to return Era from your trash to use the effect turn after turn (although it takes a lot of ener). No Limit doesn't have anything, but it's aggressive enough to not care as much. It takes some getting used to, and on average you'll still end up taking more damage from LRIGs than is usual in games with Key-format decks, but it's not as miserable as it might seem, given you've cut the number of Servants in your deck in half.
Questionable inclusions and anti-synergy weirdness
What is Rin Shizuka doing in the Nijisanji deck? She adds cards from your deck to your trash, but that's not a theme the deck is really built around at all. Sure there's a few ways to bring SIGNI back from the trash, but by level 3 you'll have plenty of cards in the trash just by paying ener costs. And this deck can't even trigger her up ability, and even if it could it only helps add more cards to the trash, which again, this deck doesn't need. In a similar vein Kaede Higuchi in Niji and Assylen, Natural Stone in Ancient Surprise both don't really help: Kaede's effects don't really accomplish much, and Assylen discards on an attack, which is nice, but there's so much card advantage that one or two isolated discards makes no real difference to the game. These decks are scatterbrained in a way we've not seen in any previous Wixoss starters, and I think (charitably) the reason is they want to give a base for modifying them. Fortunately they still play fine out of the box (Wixoss's core rules and mechanics are really robust), but several of the cards that look like they should have relevant effects will be acting as vanilla, text-less SIGNI in most games. These decks already have more vanillas than usual - the two multicouloured SIGNI, and Ancient Surprise and No Limit have a vanilla SIGNI with a powerful life burst (Sen no Rikyu, Verdant General, etc) - so this leaves the gameplay at a much more basic level. In that sense they play a lot like the first wave of introductory starters way back from the start of the game (White Hope, Blue Appli, etc), so if you're coming from the more advanced Key decks, adjust your expectations accordingly. The games are still good and involve a surprising amount of important decision-making and planning, but they're not the precision machines of Key.