There's not a huge difference, but both graphics cards are terrible. Intel names their graphics cards using a numerical hierarchy. The hierarchy for Intel graphics from best to worst goes as follows:
- HD Graphics 5000
- HD Graphics 4600
- HD Graphics 4400
- HD Graphics 4200
- HD Graphics 4000
- HD Graphics 3000
- HD Graphics (Haswell)
-
HD Graphics 2500
-
HD Graphics (Ivy Bridge)
- HD Graphics 2000
- HD Graphics (Sandy Bridge)
- HD Graphics (Bay Trail)
The words in parentheses just refer to the architecture/generation, i.e. i3-2xxx was of the Sandy Bridge architecture and came 1 year before the i3-3xxx which is of the more recent Ivy Bridge architecture. The two GPUs in bold are the one's you're debating over. Basically, both are near the bottom of the chart, and both perform very poorly (really, all Intel GPUs perform pretty poorly) so it's hard to say how well they'll perform in League of Legends. But League of Legends is the farthest thing from a demanding game. If I had to guess, I'd say at medium setting at 1280x720, you'll get between 20 - 50 fps for either card. They're both exceptionally crappy.
If I could recommend you a card, I'd actually say stay away from Intel if you're looking at integrated graphics. If you're looking to build a PC, then go with an AMD APU. Graphically, they're leagues ahead of Intel (that league pun wasn't intended).
Here's their best APU (CPU + GPU) so far:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
UPDATE: If you really want to stick to Intel though because you currently have an Ivy bridge motherboard or something then I'd say find something with HD 4000 Graphics at least. Here, the i3-3225 is still Ivy bridge and has an HD 4000 GPU which will at least give you more bearable frames in games than either the HD Graphics 2500 or the HD Graphics (Ivy Bridge) could:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
UPDATE 2: And obviously, the most optimal thing for you to do would be to actually buy a separate
dedicated graphics card. For example, the AMD Radeon HD 6670 combined with whatever CPU you currently have would dominate league. You'd actually save money this way and have a better graphical experience then either of the other suggestions I mentioned:
http://www.newegg.com/Product/Product.aspx?Item=N82E168...
I have no idea why I didn't suggest that earlier. If you're looking for a graphical performance upgrade and you already have a CPU and everything, then the HD 6670 would be your first bet as it's infinitely better than anything Intel has to offer, and it's better than the integrated graphics in the AMD APU I recommended earlier as well.
I guess I should ask, what's your current setup? Because if I know that then I can tell you the best route to go considering your current hardware and what you'd need to upgrade or not upgrade for a good experience in league.