[Samsung Galaxy W I8150] arsradu:
That is correct. The I9305 has 2GB of RAM.

So between the two of them, if I were to choose, I would still go for the S4 Mini due to the smaller form factor (it's easier to grip) and better build quality compared to the S3. But overall, the S3 is better in terms of specs. At least on paper. So let's see how much those count.

Even though the S3 is a quad-core, it's clocked at 1.4 GHz, compared to the 1.7 GHz on the S4 Mini. And, if the apps you're running are not optimized for multi-core performance (and, for as far as I know, most of them are not), it will still use only one core (the first one), which means that you want better clock speeds/core rather than more cores.

And the benchmark tests I ran when I bought my S4 Mini can prove this. The S4 mini, even though it is a dual-core, got better benchmark results than the S3 (screenshot attached). And yes, the benchmark results are not always relevant. But even in day to day performance, I felt the S4 being smoother and overall better than the S3, and I believe that's exactly because of the higher clock speed of the CPU.

On the other hand, the S3 LTE (I9305) seems to be scheduled for the 4.4.2 update. The S4 Mini also got updated to 4.4.2. BUT if you're buying the phone just for the update, you might be better off with a Nokia 3310. Cause TouchWiz is still not optimized to run smoothly on Android. So...even though the phone can, the interface (in this case TouchWiz) can't.

In my tests, the S4 Mini scored about 19700 in Antutu, when still running stock 4.2.2. Now I'm on CM11, and I got around 20800 in Antutu. Still on top of the S3, despite its better "on-paper" specs.

Some things to consider:

Display

The S3 has a slightly bigger screen and resolution (bigger screen doesn't necessarily mean better images or viewing angles. It's not always a good thing. But it depends on your taste). You've got 720p on the S3 on a 4.8" display (306 ppi) vs 540p on the S4 Mini on a 4.3" display (256 ppi). In real life, the difference is not that noticeable between 306 ppi and 256 ppi. So, to me, if it looks good in real life, it doesn't really matter if it's 256 ppi or 306 ppi. I'm not counting pixels all day long. All I care about is the overall image quality.

Features

The S3 LTE (i9305) has NO FM RADIO. The S4 Mini has FM radio.

Storage

1. The S3 LTE has 16 GB of internal storage (probably about 13 GB available for the user). The S4 Mini has 8 GB (5 of which are available to the user). Both support expandable storage.

2. S3 LTE has no IR port. The S4 Mini has IR port (for the remote control). Not a big thing, in my opinion, but it's worth mentioning.

Memory

The S3 LTE has 2GB. The S4 Mini has 1.5 GB. Not a big difference, in my opinion. But it's worth mentioning.

Battery

2100 mAh on the S3 LTE vs 1900 mAh on the S4 Mini.

Final notes:

If the S3 is selling for a cheaper price than the S4 Mini, go for the S3. If the S4 Mini is selling cheaper, go for the S4 Mini. They are both good phones and they both got their pros and cons.

If you want FM Radio, go for the S4 Mini since the S3 LTE has no such thing.

If you want a slightly bigger screen with better resolution (though you might not be able to tell the difference in day to day use) go for the S3.

If you want more internal storage (though if you're planning to use a MicroSD card, the internal storage is not that relevant) go for the S3. No matter which one you choose, I would still recommend putting as much of your stuff as possible on the External SD card and leaving the internal memory as free as possible. It does affect the overall performance.

If you want more RAM (though the difference between 1.5GB and 2GB is not that big), go for the S3.

If you want a slightly bigger battery capacity (depending on your usage, bigger might be better for you), go for the S3.

If you want a better build quality (I've got a lot of friends who dropped their S3 from pocket level and needed to replace the display, which is not either cheap or easy to do) go for the S4 Mini. The screen is a bit smaller, but the phone is simply built better and that metal rim around the display does make a difference in case of impact (at least for corner and sides impacts). If you're choosing the S3, I would suggest putting a rubber case on it as soon as you get it.