Hi,
Good question.
Most likely the number in TF is too high. Did you try loading the file up in Climbing Analysis to see what different numbers come up? I would guess that the "Training Center" setting there might be closer to what Strava computes. Basically they are probably filtering the data in a simple way.
On the other hand, it may just be a difference in GPS units -- many Edge units are known for inflating climbing numbers.
I haven't compared too many rides on Strava lately (haven't uploaded any for a couple years) but probably will this winter. It'll be interesting to see how they compare.
Scott