Icons are very pixelated with some icon packs I'm using Aviate at the moment and was trying to apply a new icon pack. While some packs are fine, most are awfully pixelated on my phone. In the following screenshots, the top screen is my 3.5' phone and the bottom one is my friend's 4.5' phone. I'm using "Blitz icon pack" here, but many other packs do this. "Sense 5 icon pack" for example, works fine on my phone.

Is this a hardware limitation? Is android incapable of anti-aliasing icons when they get resized?
I don't know enough about Aviate to know for sure, but I can guess based on the way icons normally work in Android.

An app's icon has different versions for different screen DPIs, so there's no need to resize nor antialias icons. Note that antialiasing isn't the answer here: it works by blurring icons, so they still look wrong, just in a different way. The stock Android launcher always uses the right icon for the screen's DPI. (Actually, it uses the icon one size up, because it displays the icons larger than in early Android versions when the launcher icon sizes were set.) If the app doesn't come with an icon in the correct size, it uses a smaller icon. That's why, if you have what Android calls an xhdpi screen (240 dpi or above), some apps will have smaller icons: it's because they don't have an xxhdpi icon.

From what you describe, it looks like the icon pack that's giving you trouble doesn't have any icons for your screen resolution. Perhaps the author of the icon pack didn't realise about the different DPIs. Perhaps it's some limitation of the icon pack format, which isn't an Android standard.

When this happens, Aviate is picking the next smaller size and scaling up. There's no reason they couldn't use linear or cubic interpolation to replace the jaggies (yes, that's the technical term) with blurriness. If they're using the standard ImageView component, it's just a question of setting a flag on it when the icon size is wrong. However, that would be slower, and they'd need to be careful to only do that when the icon is missing. It's possible there's some reason within Aviate that they couldn't do that; OTOH, it's possible they've just never tried using icon packs with missing DPIs, or they want to make it obvious to encourage icon authors to do the right thing.