I agree with the existing answers that the second form is better because it does not have any side effects and is easier to parallelise (just use a parallel stream).

Performance wise, it happens that they are equivalent. See below the micro benchmark results:

Benchmark                   Mode  Samples    Score    Error  Units
c.a.p.SO28319064.forEach    avgt        3  226.456 ± 56.365  ms/op
c.a.p.SO28319064.map        avgt        3  228.389 ± 25.179  ms/op

Finally note that your second snippet can be written in a sligthly more concise way with method references and static imports:

myFinalList = myListToParse.stream()
    .filter(Objects::nonNull)
    .map(this::doSomething)
    .collect(toList()); 

I agree with the existing answers that the second form is better because it does not have any side effects and is easier to parallelise (just use a parallel stream).

Performance wise, it appears they are equivalent until you start using parallel streams. In that case, map will perform really much better. See below the micro benchmark results:

Benchmark                         Mode  Samples    Score   Error  Units
SO28319064.forEach                avgt      100  187.310 ± 1.768  ms/op
SO28319064.map                    avgt      100  189.180 ± 1.692  ms/op
SO28319064.mapWithParallelStream  avgt      100   55,577 ± 0,782  ms/op

You can't boost the first example in the same manner because forEach is a terminal method - it returns void - so you are forced to use a stateful lambda. But that is really a bad idea if you are using parallel streams.

Finally note that your second snippet can be written in a sligthly more concise way with method references and static imports:

myFinalList = myListToParse.stream()
    .filter(Objects::nonNull)
    .map(this::doSomething)
    .collect(toList());