I've just finished watching Il Mare yesterday. And I've watched The Lake House some time back.
For those who don't know, Il Mare, which is "sea" in Italian, is a Korean movie made in year 2000 starring Jun Ji-Hyun as Eun-joo, a cartoon voice actress, and Lee Jung-Jae as Sung-hyun, a construction worker cum Architecture student. The Korean title is actually SIWORAE, which means "時越愛" or "Time Transcending Love". And The Lake House is a year 2006 remake of Il Mare starring Sandra Bullock as Kate Foster, a doctor, and Keanu Reeves as Alex Wyler, an architect. It's about a lady who has recently moved out of a house, leaving a letter in the mailbox for the next tenant to tell him to forward her mails to her new address. Strangely, the letter goes back in time to 2 years before, to the previous tenant instead. Slowly they fell in love with each other.
Personally, I think both movies are great, with Il Mare slightly tipping the scale due to Jun Ji-Hyun. Il Mare focused more on the 2 lead characters with Eun-joo living in year 1999 and Sung-hyun living in year 1997. While The Lake House tried to develop more of the supporting people, with Kate living in year 2006 and Alex living in year 2004. The ending is slightly different. I don't really like both ending.