Master trusts are more complicated but it is all done at a high level and you don't see it, it is carried out by the administrators of the scheme. From an policyholder point of view, things are the same as before.
As for online trading, there aren't a lot of providers that allow you to trade on your phone for your pension. Davy probably allow it (I don't use them as a provider myself, so I don't know for sure).
Buying shares directly v company pension? The income you receive to buy the shares is after tax, so you are immediately down -52%. Liable to CGT every time you sell as well as income tax, USC and PRSI on dividends versus no CGT, income tax, USC or PRSI within a pension.
Steven
http://www.bluewaterfp.ie (www.bluewaterfp.ie)