Now, from a quick play of both League of Legends and Heroes of Newerth, they both seem like the same, DoTa type game. DoTa, HoN and LoL all include the same main game-play elements, killing creeps and heroes along lanes which allows you to progress through hostile towers which defend the base. Although the games are the same in a way, they both have positives and negatives which can make a decision in choosing one to play quite difficult.
League of Legends is a free-to-play game with micro-transactions which allow you to buy many champions and their skins. Note that you can get the characters through playing the game as well.
Heroes of Newerth is a $30 game which, unlike LoL, comes with all available heroes. There are 'Goblin Coins' though, which you can purchase with money. These let you buy a wide range of cosmetic features.
Both LoL and HoN are based on DoTa, although HoN is a much closer clone to it than LoL is. In LoL, you cannot deny creeps, which in DoTa would give the enemy less gold and experience. LoL also doesn't allow creep blocking to occur. Creep blocking is when at the beginning of a match, you block your creeps so they move slower, thus forcing your enemies creeps farther into your side of the lane and allowing the tower to attack them. In HoN, both these mechanics are implemented. HoN also has graphics which add more realism to the environment than LoL does.
HoN is mainly based around more competitive style gaming, attracting players from DoTa, which in turn created a community which rejects players who are inexperienced. Since stats are put on public display, most players are out to achieve the most kills and least deaths to show they perform well, which causes the players who aren't that great to be avoided.
LoL has a more laid-back community and allows users to be more social to each other. However, due to its less-competitive nature it allows champions to be unbalanced, causing many problems for the 'serious' gamers. LoL doesn't have the best ability to reconnect to matches either. If your game closes for some reason, you cannot rejoin the game you were in and you will be forced to have a +1 leaver status to your name.
HoN and LoL both have a similar nature in play-style, yet they both attract their intended audiences, HoN being the serious gamer and LoL being the laid-back, casual gamer. Both games are made incredibly well and I would suggest that you try one, if not both of them.