I wouldn't bother with the Scotrail one at Edinburgh if you are going that way, haven't tried the EC one - their staff being quite active in making sure you don't find it being the main reason.
I am travelling from Aberdeen to Dundee, there is a lounge at Aberdeen.
I have used the EC lounge at Edinburgh and there was no-one there when I went there but I found it to be really good, there are food & drink facilities, a screen showing departures and a TV stuck on news channels.
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What benefits do you get with East Coast compared to Scotrail ?
Just one end of a carriage with a trolley, hot drink and biscuit.