There was a Goal.com article recently comparing Roma to Arsenal. While obviously no two teams will match up....here are the comparisons between the Big Fours of England and Italy.
Inter-Chelsea
Both teams have generally been the "other big 4 team" and did not have much domestic success until recently. Big spending by their new owners has resulted in some domestic dominance, but both teams are widely resented for similar reasons. Neither team plays particularly "sexy" football.
Juventus-Manchester United
The powerhouses of both leagues, both teams have the domestically dominant team for much of their history, and are one of the most famous teams in the world. The duo play a pretty middle-of-the-line game, neither free-flowing but not particularly catenaccio-esque. (barring Capello's term) Despite being the league heavyweights, both teams have failed to extend that kind of success to Europe. Both are located in the industrial capitals of their country. (Note: I hate Manchester United) Both are the most popular, and most hated teams in their country.
Roma-Arsenal
Read the above article for a more coherent take on it, but it's pretty easy. Moderately successful, both teams play attractive football but potentially at the cost of silverware. The duo have good managers who have an eye for good transfers, and are generally considered financially weaker than the other clubs.
Milan-Liverpool
Pretty easy. In the last 15 years or so, both have sucked domestically, but dominated in Europe. Oftentimes, the managers don't even seriously try for the league title at the start of the season. They envy Juventus/Manchester United's recent domestic success, but have plenty of European titles to keep their fans happy. Both managers promised to fight for the league title next year.