Unfortunately, neither your LMP nor a 19 week u/s are very accurate at dating, so either one or something in between could be correct.
Last pregnancy, I had a dating u/s that coincided with my charting-based date (the two dates were only 2 days off from each other), so we knew my dates. At the 20 week u/s, baby was measuring 22 weeks. The OB did NOT change my dates, since we had the more accurate u/s done at 7.5 weeks. Baby came at 36w6d weighing 7 lbs 4 oz (average newborn size for a 39 weeker, probably), and he was covered in vernix and had some preemie-like tendencies as you would expect from a 37 weeker. So basically, he was a slightly bigger than average baby for gestation, hence why he measured 2 weeks ahead on the 20 week u/s.
Now if I'd gone by my LMP, I would have been 9 days off on my dates, since I had long cycles.
Anyway, I'd suggest going with the new date to avoid inductions, BUT keeping in mind the original date in case things happen "early" based on the new date.