For the most part,cost is the biggest disadvantage and the largest advantage is reader quantity and consistency.Much of today's population,still prefers to sit and read a printed version of a magazine or newspaper (something about the feel of the paper) and therefore,you have large groups of people reading cover to cover.
Apart from costs,the disadvantages of print are that people aren't often times in front of a computer which limits your chance of them visiting your site,calling or emailing.
My suggestion - forget advertising in magazines or newspapers.Start a good online marketing campaign that targets organic,paid and social networking areas.It is cheaper,traffic is better targeted and the run time is much longer than a few printings.