In general, the main differences, in my view, are:
1) Harder to build a personal rapport with the interviewer over skype, which may disadvantage you. However I have also seen that most people will try take this into consideration when evaluating a candidate (e.g. "was slightly awkward but could be because of skype interview)
2) You are at higher risk of being put off / disturbed by bad tech - e.g. bad internet, microphone not working, etc. While obviously you won't be directly penalised for this, it will be hard to really shine if your interview is interrupted. You may also not be able to complete the interview, or may out of stress perform less well in answering questions.
You do not have to take any additional care in taking notes or doing calculations in the F2F interview. In fact I would advise you against trying to do calculations in your head unless you are super comfortable/it's a super simple calculation.