It has a matter of personal taste in it if you ask me, the difference between the two is not huge.
Lambdas are really good for stl algorithms, while private methods, are not as comftorable for that, on the other hand, i find private methods much better if you want to reuse your code.
This question shows the best usages of lambdas imo : lambdas
Personally, i prefer private methods, espessialy in the case you presented. Lambdas should not be used instead of private methods. It clutters the function's body and diverts the eye from the main logic.
Although it unclutter the class, it clutters the function, which i find worse.