As mentioned, this really comes down to what your intended use is.
The Model 10 in the 6" configuration is more of a range gun that can be used for defensive work; conversely, the Model 13 is a fighting gun that can be used for plinking. Both guns will somewhat outshine the other in their primary purposes.
Mechanical and cosmetic condition of each, and the asking prices, are unknowns thus far, and play a considerable role in decision making.
The shooting dynamics of each might be a wash. They're both K frames, and sporting the same grips will feel quite similar in the hand. And I'm not certain, but the heavy barrel of the 13 against the longer barrel of the 10 might yield a similar balance and weight distribution overall. For setting up target shots, the 10 will give you a longer sight radius; for close quarter defensive shooting, the shorter 13 will probably point more naturally.
It's not quite apples and oranges here, but it's nearing it.
Given that's you've wanted a 13 for quite some time, and it's a very versatile platform (from the range to the nightstand to the hip, and uses both .357 and .38), that might be your best bet.
They're a little harder to come by at the moment, and that seems to have brought up prices some, but with patience you can find one in good condition at a fair price. And keep your eyes peeled for a Model 65; it's the 13's stainless twin.
Alternately, don't rule out the heavy barreled Model 10s and 64s; if you don't need or desire .357 capability, these models are otherwise identical to the 13 and 65, are easier to find and generally at better prices.
So, it comes down to intended use: how will you use the gun?
