If poeople say that they play worse golf with a leccy trolly or the to the same standard then it is purely a mental thing.

There is no way that any single person (even a modern day athlete) would not physically 'notice' the difference between an electric trolly and a carry bag. Even if they did not feel it due to the mental issue, if you ran a few simple tests such as heart rate / pulse / recovery time on latter holes there would be a difference. 

I use the Clicgear 2008 push trolley and can highly recommend it. Don't go for the old pneumatic tyred model as the tyres are too narrow. Mine feels light as a feather with my (not at all lightweight) Bagboy revolver bag and full set complete with umbrella, retriever, waterproofs, drinks and food for 18 holes. 3 big 12 inch wheels, umbrella support, storage for spare balls, scorecard holder and GPS (not got one thats the next item on the purchasing agenda). Very well built and should last a lifetime (for me at any rate). Well worth the money.

An extra benefit is is that it looks quite intimidating so could be worth a couple of extra shots per round!!!!