[Nagoyankee]

The only difference is that you will hear the first sentence much more often in conversation than in writing. Likewise, you will be using the second sentence more often in writing.

This has nothing to do with politeness. If you want to add any 'politeness', you do it with the other words, and not with の or　こと. By 'the other words', I mean お友達、お話しする、しております, etc.

I often hear Japanese-learners say "Verb + を" without の or　こと. That sounds very foreign to us. It's often the smallest words (in many cases, particles) that make your Japanese sound better or worse. It's rarely the big words.