So, I got into the closed beta for this, and I thought I'd provide some thoughts on it for those who are fans of MOBAs.
My experience with MOBAs isn't huge. I did play quite a bit of League of Legends for a while, and I have tried out DoTA2 (I played the original DoTA mod, but very, very little of it). So I'll mostly be using LoL for my base of comparison.
Overall, I like it. It makes some pretty significant changes to LoL's formulae. Some of them definitely help, others are a bit harder to rank.
One of the biggest early changes is the lack of an ability unlock system. This is simply fantastic. One of the biggest problems I had with LoL was how boring it was to play in the early game (especially for Carry characters, who I enjoyed the most overall). You were stuck with such limited utility that the entire first part of the game just felt like a grind to get to the point that you would actually start playing, which was halfway through the match. In Heroes of the Storm, you start with all of your abilities unlocked (except your ultimate), and you simply gain bonuses to them, or change the way they function, as you level up.
The level up mechanics have also been completely revamped. Teams now gain levels altogether. Experience is awarded for every kill within proximity of a hero, but this experience goes to the entire team. This means that you'll want each lane covered to make sure you keep the experience flowing, but you're no longer penalized for covering a lane away from the action, or doing one of the bonus objectives (which vary by map).
Jungling has been massively overhauled, and I definitely like the Heroes system. Instead of fighting creeps for gold, experience, or buffs, you fight creeps for their allegiance. There are far fewer mobs, and they're more difficult. But, when you defeat them, if you stand in their camp for a brief time, they'll join your force, adding their strength to the closest lane. This massively changes the dynamics. If you get down time, rushing to a camp, taking down the foes, and getting back into place has a significant impact on the constant tug-of-war. The camps respawn slower, so you're unlikely to have a hero jungling constantly, but when you can pick up a mercenary camp, it's worth doing so.
Many maps also have bonus objectives. In one map, there's a mine that you can run into and clear creeps from, earning points towards summoning a large undead golem for your team as you do so. It makes that map have a bit of a more traditional "MOBA jungle" feel to it. On another, a temple will temporarily turn on that acts as a powerful turret, attacking minions and even bases while it is active. So capturing it by defeating its guardian is a pretty strong incentive, though it isn't a make-or-break for victory. I still have yet to go through all the maps, but they all look to play differently and interestingly.
One of the biggest changes that MOBA veterans will notice: There is no gear. This actually shocked me at first. I was wondering if it was locked for the tutorial, but it just looks like the gear system is gone entirely. I have some mixed feelings on this. On one hand, I loved the sense of customization and control it gave you over your character, as well as the significant feelings of progression it added. On the other hand, everything else about it sucked. There were so many options to choose from, but there were only a handful that were actually useful for any given hero. There's a reason that half of the LoL community is centered around build guides. There are some pretty clear and defined "best items", and those vastly overruled personalization. It also added to the problem I mentioned at the beginning: Early on, your character was less fun to play because you didn't have those item buffs.
There is a definite gameplay benefit to leveling up in Heroes of the Storm, though. In addition to just doing more damage and having more health, every few levels, you'll get a choice of ability. These abilities are modifications to ones you already have. It can increase the range or AOE of an ability, or add a bonus effect to another. You start with only two choices for most of these, but as you use a particular hero more, you'll be able to get up to four choices, giving you a pretty decent degree of choice. This new system really appeals to me personally. Everything about if keeps you focused on winning. When I played LoL or DotA2, I was playing to fit my hero out the way I wanted, get my gear set and levels up, and I frequently didn't want to win because it would mean starting over in a new match as a boring starter hero again. Heroes of the Storm centers everything around progressing the match, and I find it makes for a much smoother gameplay experience overall. I was enjoying winning far more than I did in LoL or DotA2.
Finally, there's the tutorial. This is brilliant, and it really makes me sad that there isn't a full campaign mode. We have Jim Raynor yelling at Diablo that "it is just not possible to consume or taste fear or terror", and Diablo getting mad when Stitches backs Raynor up on this "fear no have taste". The tutorial is well paced, introduces you to concepts quickly, and is incredibly well written. There is so much potential for a full mode here, it's definitely going to be one of my biggest suggestions to Blizzard when responding to the beta (apart from the bugs and other issues I find, of course).
So, overall, I like it. It is a more noticeable shift in the MOBA standard than I thought DotA2 was, and I personally prefer playing it quite a bit more. I just think it's a bit better structured and focused. Is it enough to keep my playing any more than I do MOBAs overall? Maybe not (unless it gets a campaign mode, in which case I'll be playing it for a long, long time). But it's definitely worth keeping an eye out for if you're a fan of the genre.