Swimming is a more hypoxic form of aerobic training than running because you breathe less often, so it trains you to tolerate higher levels of CO2 in your blood while performing aerobic exercise.
It will also improve the muscular strength and endurance in your back and arms, while running will not do that at all.
As far as cardiovascular benefits I would assume that you need to work in the same HR ranges as you would running to get the same benefits.
From my own experience swimming laps, the most immediate improvement I noticed was the ability to swim faster (i.e. greater power output at higher HR) and for more laps before that burning discomfort of needing to stop and catch breath, or slow down, kicked in.
edit: I don't have experience doing both at the same time regularly, I was only swimming laps because i injured a knee and couldn't run for a few months.
However, when I was younger i used to surf a lot and back then I could hold my breath for 2 min. Now, I have a RHR of around 50 but I am training quite regularly, but for about 5 years riding waves was the only exercise i did. Make of that what you will.