Sputtering transmission on my E320

[1995-E320-Owner]

I own a 1995 E320 with 136k miles on it.

I bought it used in 2003 with 117k miles, and since I've owned it, I've noticed a slow, gradual decay in the acceleration. For instance, from a dead stop, if I press down the accelerator even just mildly, I have maybe a 1 in 2 chance of getting a normal start; otherwise the drivetrain sputters and struggles to increase power (I usually have to lay off the gas for a moment and try again).

Lately it's been getting more pronounced: now it happens when I am moving in traffic, and if I suddenly need to put the foot down on the gas to accelerate out of a tight spot or something, sometimes the engine can't give me the power I was expecting --- I wind up with this sputtering, unsure engine/trans that's getting me very concerned.

Is this a transmission symptom? Is it time to service the trans, or rebuild, or replace? Is this an engine prob, or something else?

Any ideas/advice would be appreciated.