Up to last season (2008-09), both were pretty evenly matched. In the 2009-10 season, however, Chelsea have been much better.
Chelsea won the the Barclays Premier League while Liverpool finished 7th. Chelsea reached the quarter finals of the UEFA Champions' League while Liverpool crashed out in the group stages.
Liverpool had a great run of success in the 1970s and 80s, and they have won the top flight competition for a record 18 times. Liverpool also have a far better record in UEFA Champions' League, winning the competition 5 times, whereas Chelsea's best record came in 2007-08 season, reaching the Final, where they lost to Manchester United in penalties.
In the recent years though (Since Jose Mourinho took charge in 2004-05), Chelsea have been performing much better than any other club in England, winning 3 Premier Leagues, 3 FA Cups, 2 Community shields and 2 Carling cups. Interestingly, Liverpool have never been able to lift the Premier League.
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Historically and overall, Liverpool because they have a well-rounded offense and defense, and even though they are slacking lately, Arsenal would be near relegation zone without striker Robin Van Persie.