Actually, balance isn't the issue with league... It's that base champion stat scaling is awful, and champions have different numbers of well-scaling damage abilities, which causes huge individual peaks/fall-offs at different points in the game, and very few champions have a consistent ability to perform throughout the game, which can make it incredibly punishing to play the laning phase against/as certain champions. Also, mobility and CC... some champions have way the fuck too much of it (Riven and Lee sin for example... Leona as an example of too much CC; 3 CC abilities...) and true damage shouldn't exist in a game that revolves so much around non-health defensive stats, especially % max HP true damage (Vayne/fiora), even if the champions with it are balanced because of vulnerabilities, it's a terrible mechanic to have in the game because it nullifies necessary defensive stats.
In addition, items are excessively powerful relative to base stats/ability damage, which pushes ~50-90% of champion damage output into items (depending on build; it's ~90% for ADCs, and can be similarly high for full glass mages; for tanks it's closer to 50%, assuming ~1.5-2 damage or hybrid tank/damage items), and the same is true for Effective HP, albeit not quite as extreme in the numbers. I would probably consider league a better game if there were no items/runes/gold (assuming it was reasonably balanced), because it would tone down the disparity in champion performance relative to the time of the game, and would make damage output/defense much more reasonable, which would also help balance the effect of CC and mobility, since mobile champions wouldn't be able to 100-0 bruisers with 3 defensive items and get out.
In HoTS, Hero scaling is rather consistent throughout the game, with few heroes having excessively powerful peaks/fall offs, and with team-wide exp, there isn't a period in the game where one person can snowball into becoming god of that game for 10+ minutes (Which is the most frustrating part of league IMO; it's not fun to be that person that's stomping everyone, and it's not fun to play against it), and with no items, the disparity in stats doesn't get so extreme; carries aren't dealing 10x the damage of tanks, but they also don't have 1/10 the survivability; it's more like damage dealers have ~150-250% of the damage and ~40-60% of the survivability.
Also, the game is relatively new, so it would be rather unreasonable to expect particularly good balance, which overall, isn't much worse than LoL's when you consider the number of characters that are strong/viable relative to the total number of characters.