Ascension: Storm of Souls (SoS) is the second Ascension game. StoneBlade Entertainment has a rather confusing system of releasing a stand-alone Ascension game and then the next year releasing an expansion for that game, and also a new stand-alone game. These games are not numbered, and can all be mixed and matched as you see fit. SoS is a full stand-alone game that can be mixed with any of the other games or expansions, but is officially paired with the expansion Ascension: Immortal Heroes (IH).
SoS continues to use the 'Fate' mechanic introduced in the previous expansion, Ascension: Return of the Fallen. However, it also includes two new minor mechanics. First, a new type of monster, 'trophy' monsters, which allows you to save the rewards for defeating certain monsters until the time of your choice, and in some cases, to reuse the reward for the rest of the game. To go along with this, the Cultist is joined by a Fanatic, who can be conquered for three attack and saved until needed to trigger the current event.
Events, of course, are the other new mechanic. These are simply faction-linked rules that are in play for a random length of time (certain cards will instruct you to draw a new event card when they first appear). Events tend to tilt the game to benefit one faction over another, e.g., "the first hero played each turn is also a lifebound hero". They usually require some thought to use effectively. Additionally, they all have a special effect that is triggered by the Fanatic, usually nothing too impressive. SoS has a very limited set of event cards (5), although the IH expansion will help fill this out with another five.
I believe that SoS is also the first set to specify cards with 'unite'. While this has been a mechanic since this original game, it has not been clearly stated as a separate effect on cards, and SoS fixes this, for the simple reason that the Lifebound faction is going to start using it more. (This will be particularly true in Ascension: Realms Unraveled).
SoS continues the trend of diluting Mechana's effectiveness, to the point that specializing in Mechana is no longer a winning strategy. Given the effectiveness of synergizing Mechana in the original game, this is a bit of a letdown. They attempt to balance this by introducing the most powerful Mechana construct yet (P.R.I.M.E.), which is frankly overpowered (but fun if you get it!). Meanwhile, SoS has more high cost/high power cards than earlier sets, and the lower price cards are a bit underpowered, which means it takes a bit longer to get a powerful hand. Building into this, banishment cards are significantly less powerful. This leads to a much slower start to the game.
The endgame, however, can be quite exciting. SoS has the most overpowered hero yet, Avatar of Aiyana, which allows you to acquire heroes from the center row very cheaply. There are a number of other powerful cards that can synergize in profitable and amusing ways, particularly if you are mixing decks.
I very much prefer mixing multiple games together, and therefore have very little experience playing SoS on its own. It mixes very well with the original Ascension, and I generally recommend starting with the original Ascension whatever your expansion plans may be. However, it is designed to function as a stand-alone game, and the few times I have played it as such I had no major complaints. However, I do think that the faster gameplay of the original game is both better in general and especially better for new players.
But this does give SoS one major benefit. If you originally purchased the Apprentice Edition (AE), SoS is a great next purchase, giving you a full base game to mix with your AE, and filling out SoS's weak points.