try to do: -てみる vs. volitional+とする

Although both mean "to try to do something", there are some nuances involved, and the two are not interchangeable. Thanks to Elenkis' post here, I finally got a decent explanation for this.

1. -[te form]+ みる is used when you are trying to do something because you want to see what happens afterwards. The emphasis here is on what happens if you try.

2. -[volitional form of verb -おう or -よう] + とする , on the other hand, emphasizes the fact that you are going to try, regardless of the result. Note that  In fact, a similar construction (-ようとした), indicates failure ("I tried..., but I failed.).

As Elenkis said, there is a difference between  “I’m going to try drinking sake (and see what what it’s like)” and “I’m going to try to finish my homework tonight”.

Other similar constructions are [plain non-past form]+ ようにする. Another is [plain non-past form] +ことにする.

3. [plain non-past form of verb]+ ようにする means that you put your mind on something, and you're going to exert all effort, even if you fail, until you reach your goal.

4. + ことにする means that you have decided on doing something. It can refer to a single or a habitual action. This seems close to the construction  -[volitional form]+と決める（きめる）, as mentioned by Tae Kim, although I haven't heard or read the latter used.