You would have been better off saying that you couldn't tell the difference then, not saying they were basically the same.
Right off the bat, the battery life was much better, it wasn't even close with standby time being literally days longer, talk time was in the neighborhood of 6 hours longer, some tests had it in the double digits. That's about as drastic as you can get when it comes to battery life in a cell phone. It's silly to say there is no difference between the two.
Never mind that benchmarks in processing are almost double of the S4, saying these two phones are the same but one is bigger is silly.
Also, sPen may seem gimmicky to some but to those that use it and learn to use it, you'll get so much more functionality out of your phone it's silly.
I don't want to get into a massive argument here, but I actually owned both phones. I had the Galaxy S4 from April '13 to Sept '13 when I broke it, so about 6 months, and I've now had the Note 3 since last October, so about 6-7 months. Battery life is better on the Note 3, but not drastically so. Yeah, maybe if you do a test of purely idling it'll last a lot longer, but who doesn't use their phone for days at a time? No one, that test is useless.
My usage is similar most days, the vast majority of my usage is data-based(internet browsing and email), I don't make a lot of calls. At the end of the day my S4 used to have about 1/3 of it's battery left on average. My Note 3 is now usually in the 40-50% range at the end of most days. Sure it's better, but drastically so? Not really. Maybe 25% better. Thats probably because almost all of my usage is done with the screen on(as opposed to talking on the phone or idling where the screen is off). I would imagine most people would have similar experiences, definitely anyone who has most of their phone usage with the screen on(internet, media, email, etc)
Heres a benchmark of my Note 3 compared to other top-end phone models & the S4 specifically:
It's definitely better. It's nowhere close to "almost double" the power of the S4. Some of the CPU-related benchmarks are maybe 10-20% higher, while a few(like 3D performance) are nearly 50% better. Nothing is anywhere close to double in any single category, much less the aggregate performance.
Look, the Note 3 is the best phone out on the market right now IMHO, I love it and I recommend it to anyone that asks. But I'm not going to pretend it's night and day drastically better than the S4. And I fully expect the S5 to leapfrog the Note 3s performance when it comes out soon.