prefer to do something vs prefer to doing something

Some examples from the web:

• Because I'm not satisfied with the way things are, and rather than sit back and moan, I'd prefer to do something about it.
• I realise you prefer to do something with a little art in it, Mr Timmins.
• Coaxing means that people prefer to do something because they see the benefit of it and I think that the Commissioner has achieved exceptional success in this.
• If you'd like to take the camera back, I'd prefer to do something.
• There will be a small event with heads of the dicasteries because he prefers to do something small, very modestly.
• No. Girls usually prefer something scented.
• I think women prefer something more personal.
• I would prefer something more final.
• She prefers to believe in something outside itself miraculous.
• I would prefer to say something different, in relation to our proposals: it is a question of Europeanising the railway system.
• Frankly, I prefer something dry.
• I prefer something simple myself, but I thought you enjoyed variety.
• You'd prefer something classy, elegant, but contemporary.
• I prefer something a bit more subtle like...
• Prefer something more... like... this?
• I prefer something that can go through me.
• My Master would prefer something more classical.
• Don't stand on ceremony, if you prefer something else...
• We'd prefer something more comprehensive, though.
• This means that many people are either indifferent or would prefer something else.

Some examples from the web:

• They wanted to dedicate their lives to doing something great.
• Most prone to doing something that he may regret.
• Devoted myself to doing something better with my life than wasting it on love.
• Did she actually admit to doing something wrong?
• Don't put yourself to doing something with him.
• I... I was this close to doing something the other day.
• The reverend just admitted to doing something that's perfectly normal that every man does.
• «She's committed to doing something meaningful,» said Venice High principal Bud Jacobs.
• There are many reasons to choose to crochet as opposed to doing something else with your time or to express yourself creatively.
• Now we don't have a great track record when it comes to doing something like this, to eradicating diseases.
• I really believe we have the citizens of the entire Union behind us when it comes to doing something about the dreadful ways in which livestock are transported.
• My eye stopped twitching, and Catalina was back to doing something she loved, which made everybody happy.
• I came really close to doing something I... I didn't think I was capable of...
• I prefer the green tea and I realize that doing something different with highly popular shellfish like scallops is an arduous task.
• We should especially encourage our non-Governmental organisations because therein lie the activists, the people who are committed to doing something to protect the fundamentals on which this Union was founded, namely peace and harmony.
• But she was... she was on her way to doing something great, like working for Elizabeth Warren or being a, an adorable, yet completely not ironic hat model.
• We need a clear, simple political text that shows that we are moving from talking about tackling climate change to doing something about it.
• Ordinary people like you, used to doing mundane and small things, finding themselves in the midst of a crisis doing something extraordinary.
• All of the eminent people happily stand there and tell everyone how much they like Europe, but when it comes to doing something and actually implementing these things, the Council suddenly has problems.
• How many times do we have to ask, urge, beseech - and I do not know what else - the Commission to get round to doing something at long last?