Do small-resolution resource/texture packs really have an effect on performance?

I've seen 8x8 and smaller resource/texture packs that claim to increase ingame fps (frames per second), but then other people comment saying that there is no difference. Who is right?

EDIT: I just found this similar thread on the Minecraft Forums: Do 8x8 Resource Packs make Minecraft Faster? (1.7.2).

Solution 1:

Neither and both. Confusing?

Here's the deal: Minecraft uses quite a deal of processing power, both with the CPU and the GPU. Texture packs are handed by the GPU.

Now consider the following: Loading an 8x8 texture is 1/4 of the load of loading a 16x16 texture (that is the default size). However (and here's the catch), despite the less work, you would only notice any difference if the GPU was bottlenecking the process. In other words, if you weren't running at top graphical performance, you may see some small difference.

The reasoning here is also valid for HD texture packs: the bigger the texture, the more load the GPU is subject to and your performance will drop accordingly.