Yes Liverpool has won more trophies and is in the Barclays Premier League, unlike Leeds who are in the Championship league below the BPL.
These are the national and international trophies Everton Football Club have won throughout their history. First Division/Premier League - 9 times Second Division - Once FA Cup - 5 times League Cup - Once FA Charity Shield - 9 times European Cup Winners Cup/Champions league - Once That's a total of 26 national and international trophies, but Everton have won a number of local and friendly tournaments also.
Barcelona have always won more trophies then Liverpool any day.
Manchester United have won much more trophies than Chelsea have.
Barcelona have won more trophies then Manchester United.
Manchester United has won more trophies than Arsenal.
37Tottenham have won a total of 26 trophies in all competitions.Liverpool have won 63.
Leeds United have won more trophies in their history than Sheffield Wednesday. They are currently in the Championship, one league above Wednesday, and were also more recently in the top flight. They have also won a European trophy, and participated fairly recently in the Champions League. There is no doubt Leeds United are better than Sheffield Wednesday in terms of pure statistics.
As of the end of the 2014 FA Cup, Chelsea have won it 7 times and Everton have won it 5 times.