It's similar, but not exactly the same. Strava uses a different formula for Weights Power (Normalized Power in Training Peaks terminology). Above-threshold efforts are more heavily weighted in the TrainingPeaks/Coggan formula than in the Strava formula. Since normalized power is used to calculate TSS and all the other metrics, that means the Strava numbers will be a little different, especially if you're doing lots of high-intensity stuff.
The other big limitation with Strava is historical data. In Strava everything is based on your current FTP setting. So if your FTP is changing, the historical data becomes inaccurate.
That's true for the weighted average power Strava reports but my recollection was the Fitness number matched my CTL number from Golden Cheetah within a few points. Whatever formula they used also worked pretty well with just HR. I didn't notice much difference when selecting power vs HR on Strava's numbers.