When you can find them, the 1951-59 run is better watching, because it's much more crime drama and investigation. If you're into history, the opening scenes are fascinating because it shows a post-WWII Los Angeles before much of the core was redeveloped. It's a lot of low-rise sprawl because a lot of earthquake-proofing building techniques were not developed yet, and Los Angeles at the time had an ordinance preventing any building from having more than 13 stories. Here's an article about that, along with a comparison of mid-1960s downtown versus 1980s downtown.

http://www.kcet.org/updaily/socal_focus/...-of-angels.html

The 1967-70 revival had a much different tone. You see it about midway through the second season (1968 or so) -- there's a definite shift away from solving crimes and more focus on the other community-related functions of the LAPD (e.g. press relations, training, community relations, etc.). It coincides with the tremendous social change at the time.

The 2003-04 remake with Ed O'Neill is on Hulu streaming. The first season is good, but Dick Wolf destroyed that series in the second season by making it into a de facto Law and Order: Dragnet.