None of the premise in that statement makes any sense to me.
1. The Note 3 has more software on it than the S5. Notes always do, because they have all the extras for S Pen functionality.
2. The Note 3 has more "frills" than the S5. That's a byproduct of its form factor, as stated in '1'.
3. The Note 3 is using an older build of TW than the S5, which is not as well optimized, and an older SoC Package.
4. With the S5, Samsung actually preloaded less crap than they did on the Note 3.
I think the extra 1GB RAM on top of TW is what gives the Note 3 the edge. Samsung should have gone with 3GB in the S5, IMO. The extra RAM seems to help TouchWiz devices disproportionately more than it helps HTC or Motorola devices, or devices running other OSes like iOS and Windows Phone.
The S5's reception is enough of a reason to get it over the Note 3. The Note 3 is terrible, and it's a common issue. Verizon's forums have been blowing up about this for several months now.
Doesn't matter if it has a Quantum Computer in it, if your SMS and Group Messages are failing left and right in your living room, you're dropping tons of calls, and the phone doesn't know how to consistently switch from 3G to LTE when traveling through areas of various reception quality (unless you toggle Airplane mode)...
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Regarding the Note 3's processing performance (as in running apps and using the phone as a smart device)...
I've always said the phone was a flagship performer - even now. The issues with it are (on Verizon) the bad radio/antennas and the bloat loaded on it. I've never had any complaints about it performance-wise, and it performs as well as my HTC One M8 did with older hardware in it. Assuming you don't have the Verizon variant, and got the Note 3 near release, it's a true 2+ year device, IMO.
So it doesn't surpise me that you (OP) notice it being as snappy or even snappier than an S5, especially since it (until the Note 4) was, IMO, the best-spec'd TouchWiz device (that extra RAM makes that much of a difference on Samsung devices).
But I got rid of mine for an iPhone 6 Plus, cause the reception is just not acceptable with it, and I already have another Android phone if I need that OS for something specific

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