A 2" steel K frame .38 is a lot lighter than any 686 (7-8 ounces under a 2.5" version). If you meant to ask about the model 60 also, as your title suggests, this weighs only 19 ounces in the 2". The alloy J frames go down to as little as 12 ounces. How much the weight matters for carry varies from person to person, but it is one of the big reasons for the popularity of J frames.
The 6906 is a little narrower across the middle than a model 64, but concealability involves several different factors like weight, holster type, etc., and only you can decide that.
Personally, if you like carrying your 6906, shoot it well and use proper self-defense ammo I would think it to be a nearly ideal carry gun; hard to argue with having 24+ rounds easily available with one spare loaded mag too. If you can afford the 64 and proper carry gear, however, why not try it out and see?