Which would offer more protection? Changing the oil every 3k with regular oil or 5k with synthetic?

With Amsoil:

I go 10,000 miles on my turbo. Oil is still OK, nitration level is a tad high so I change.

With my non-turbo the oil (Amsoil 0W-30) is still virgin at 10,000 miles. The oil is rated for 35,000 mile change intervals. Change the filter at 5000 mile intervals. Not the oil.

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http://www.fidalgo.net/~brook4/oilslubesfilters.html

In most cases, a good synthetic will offer more protection with 5,000 miles on it than a petroleum oil will right out of the bottle.

Generally speaking, 5,000 mile intervals are just fine with any synthetic (even non-PAO based ones), and are usually fine with quality petroleum oils. Like Volvospeed stated, much of this depends on your driving characteristics. On my T5, my oil is still perfectly serviceable after 10,000 miles of rigorous use, but I use a PAO Class IV oil engineered for safe, extended drain intervals. If you really want the answer to your question, you will need to spend a few dollars and have your oil analyzed. This is what I do. It only costs about $15, and really helps establish a baseline for your car.
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1999 S70 T5

Have it assayed with both intervals. There are a lot of variables like type of driving, temp, humidity, and so on. I do not think a blanket statement is appropriate.