Another difference is going to be the weight the the putter. The old TeI3 weight was around 330g and the new T22 is close to 350 grams but that can be changed. Not sure how much difference if felt between the old carbon steel head and a stainless steel head since the insert to contacting the ball.
Mostly the difference is putter head weight. The original TEI3 from 20 years ago had a 330 gram head weight. I don't know what is the weight of the new
T22 without its weights, with weights etc..., but my guess is that 340 gram head weight is the T22 with its lightest weights installed.
I read somewhere that the T22 heads are 330g empty, so the 35" with 10g weights would come in at 350g.
Not 100% sure on accuracy, but that's what I have heard.
I've been rolling a 35" Newport that I reshafted to 33.5". It has the 10g weights and to me it does feel like it's in the 350g range. I usually prefer a putter around 340g and it feels a little heavier than that.