I don't use Golden Cheetah, but I seem to recall somebody mentioning that it uses the same formula for NP as Strava, which if true would explain why you didn't see a difference. In fact I wouldn't be surprised if Strava got their calculations from Golden Cheetah since it's open-source.
I use a browser extension for chrome called Stravistix, one of the extra data fields it adds to a strava workout is "A. Coggan Normalized Power", which I've found is always higher than Strava's weighted power.
It's not a huge difference for most workouts, and as long as you know what your fitness/freshness numbers mean for you, it's probably not a big deal at all. I only pointed it out because even the Coggan/TrainingPeaks formula is more heavily weighted towards duration than intensity than it should be IMHO. A 120 TSS VO2Max interval workout definitely takes more of a toll on me than 120 TSS from riding zone 2, and the former takes longer to recover from as well.
Yes, I see they're not identical. The last few rides have the following TSS data: 164/169, 132/137, 199/205 for Strava/Golden Cheetah. Golden Cheetah uses Coggan's formulas for NP, TSS etc.
Basic trends are the same and Training Stress Balance is the same so I don't worry about the minor differences.
Neither formula is perfect but they're still useful to me. I can jack up my NP by just sprinting for 10-20 seconds every 5 min or so. I don't find these types of workouts particularly fatiguing but they can result in a high NP. Achieving the same NP with VO2Max intervals is more tiring for me.