I have both the ATT and SIM-free iPhone 7, and have tested them side-by-side over the past couple of days.
Spoiler alert: There doesn't appear to be a material difference between the phones with respect to overall performance, signal strength, LTE speed, or battery life.
One difference that seemed consistent was the SIM-free phone's propensity to switch from fringe LTE to 4G, and similarly from 4G to EDGE. I assume in these cases it is switching RF bands. It definitely prefers a "stronger" signal, which may be good for voice, but in my testing was often bad for data. The weak LTE signal which the ATT phone clung to consistently (and expectedly) outperformed the stronger 4G signal of the SIM-free in data speed tests. This behavior didn't appear in all weak-signal areas, but appeared often enough to note.
With respect to LTE speed, I suspect that the lab tests, while perhaps accurate, are practically meaningless in real-world use. There are many variables involved with data performance, most of which are outside the control of the phone. In my unscientific but somewhat controlled tests, both phones performed nearly identically with throughput in all signal areas and on various LTE bands. The SIM-free phone did seem to consistently generate lower ping times, but this difference doesn't appear noticeable in real-world use. The affinity of the SIM-free phone for stronger but slower HSPA+ bands is noticeable, though perhaps that's a fair trade-off for better voice quality. I have received repeated complaints from voice callers about distorted or sketchy voice in weak-signal areas with the ATT phone, something unusual with my previous iPhone 5s. I don't yet have enough data to determine whether the SIM-free performs differently in this regard.
As for other differences, the screen on the SIM-free is slightly warmer than the ATT phone, though the latter appears to have a slight pinkish cast to it. This difference is more noticeable in low light, but it is not drastic and likely would not be detectable apart from a side by side comparison. In any case, I suspect that screen quality has more to do with build inventory than chipsets.
JKG
Spoiler alert: There doesn't appear to be a material difference between the phones with respect to overall performance, signal strength, LTE speed, or battery life.
One difference that seemed consistent was the SIM-free phone's propensity to switch from fringe LTE to 4G, and similarly from 4G to EDGE. I assume in these cases it is switching RF bands. It definitely prefers a "stronger" signal, which may be good for voice, but in my testing was often bad for data. The weak LTE signal which the ATT phone clung to consistently (and expectedly) outperformed the stronger 4G signal of the SIM-free in data speed tests. This behavior didn't appear in all weak-signal areas, but appeared often enough to note.
With respect to LTE speed, I suspect that the lab tests, while perhaps accurate, are practically meaningless in real-world use. There are many variables involved with data performance, most of which are outside the control of the phone. In my unscientific but somewhat controlled tests, both phones performed nearly identically with throughput in all signal areas and on various LTE bands. The SIM-free phone did seem to consistently generate lower ping times, but this difference doesn't appear noticeable in real-world use. The affinity of the SIM-free phone for stronger but slower HSPA+ bands is noticeable, though perhaps that's a fair trade-off for better voice quality. I have received repeated complaints from voice callers about distorted or sketchy voice in weak-signal areas with the ATT phone, something unusual with my previous iPhone 5s. I don't yet have enough data to determine whether the SIM-free performs differently in this regard.
As for other differences, the screen on the SIM-free is slightly warmer than the ATT phone, though the latter appears to have a slight pinkish cast to it. This difference is more noticeable in low light, but it is not drastic and likely would not be detectable apart from a side by side comparison. In any case, I suspect that screen quality has more to do with build inventory than chipsets.
JKG