This was on an N3DSXL with Luma3DS 8.1 and NTR 3.5. I was using the memory patch and NFC patch (as they're required for streaming), and I was streaming the whole time NTR was active. Results:

NORMAL: continue: 3.23s/3.26s/3.33s pokemon center entering: 2.38s/2.40s/2.37s houoli city grass patch entering: 3.49s/3.93s/3.88s honey: 9.10s/9.20s/9.15s NTR: continue: 3.35s/3.36s/3.31s pokemon center: 2.45s/2.35s/2.26s houoli city grass patch entering: 4.04s/3.95s/4.00s honey: 9.38s (i hit stop a little slow)/9.14s/9.25s

Do note that, although this cannot be proven, the presumed reason for Gen 6 being faster, is that NTR needs Clock + L2 overclocking mode to stream. Sun/Moon does this by default, even on a stock console.