The difference between the two is that in Criminal cases, you are defending yourself against the government for breaking a criminal (or traffic) law. The government can be at the city, county, state, or even federal level, and is represented by a prosecutor. There is a limit to how much you may be punished for each offense, either in jail time or fines. The prosecutor has to prove beyond a reasonable doubt that you are guilty.
A civil litigation on the other hand, is much more subjective. You are being sued by a private person (usually represented by a law firm) whether for something you did (or failed to do) which may have caused them harm or cost them money. The burden of proof is 50/50, which means if the evidence weighs slightly more against you than against your accuser, you lose the case. Like criminal litigation, civil litigation is VERY costly in order to hire defense lawyers. Most lawsuits settle "out of court" at a reduced settlement cost in order to avoid paying potentially higher costs defending one's self in court.
I've never heard of Norton Rose, but I have heard of Latham & Watkins (it is a U.S. based law firm with international offices).
According to the website of the respective law firms, Norton Rose doesn't have a presence in the U.S. It has "U.S. qualified lawyers based in London or Hong Kong."
Latham & Watkins seems to have more offices in the world (including the U.S.) than Norton Rose.
Unless you find someone who has worked for both firms, it will be hard to answer your question - plus it is subjective.
Remember, big isn't always better - look what happened to Brobeck Phleger (it imploded after it got too big too fast).