Most programmers end up learning everything a network admin knows, plus they know how to program. However, the reverse is not true. Network admins do not 'pick up' programming, or if they do, their knowledge is very basic.
Programming is theoretical in nature and requires higher mental function. Real programmers usually do not learn how to program from do it yourself books. They have a solid understanding of mathematics and numerical analysis, algorithms and algorithm analysis, and know the linguistic theory behind the syntax and grammar of languages themselves. While network administration is task oriented.
You need not believe the hype,there are a lot of opportunities in both the fiels. You just need to know how to market yourself and your skills. The real question is, what are you interested in doing?
Try getting into a good internship and you will get to know it for yourslef.
Hope this helps.