Firstly, you ought to look at what your product, service or brand is and who its ideal target audience is. If you are targeting Millenials and you go into mainstream print media - you are likely to miss them. It's just not how they consume media. Or if you want to reach Baby Boomers and you focus on Snapchat.

While there is a huge argument for traditional media to be included in one's marketing mix, so is there for online marketing. And, as  I am not aware of the foundation of your question, I can not answer specifically...  However, both are relevant (generally) in today's marketing outreach and one form of marketing that is hailed as one of the most low-cost yet high-impact is PR. The likes of Sir Richard Branson and Bill Gates, swear by it. And, it usually goes across print and online and makes for great social media content (once it has been published) too.

So, as an answer to your questions, it really depends. But, if in doubt use PR. ;)

It comes down to where the best place is to find your customers.  Traditional marketing including, print, direct mail, etc. can be very effective when trying to reach an audience that tends to skew older, less tech savvy, or where lots of information needs to be processed and considered to make a buying decision.  There is no one silver bullet in the marketing tool kit so the best bet is to look at the budget and put together a realistic strategy and plan to reach your customers in the most effective ways possible.  Each vehicle has strengths and weaknesses so using a mix of tools is ideal with the right message getting to the right audience.    

Traditional Marketing is more of B2C whereas online marketing is for B2C and B2B. It all depends on the type of product or services you are offering. Suppose you are offering CRM product with free extinction or some Database related products, In this case, traditional marketing will go for a toss whereas your online marketing will work most efficiently because you know your targeted audience and their behavior and also it is the best value for money method.  

The key is to not think of them as disparate practices. The words 'online', 'digital' or 'traditional' are redundant if you're focused on the meaning of the operative part of the practice - marketing.

Focus on finding who your best customers are, why they buy and why they should buy from you. Once you have a clear idea of the answers to these questions, you'll be well placed to start looking for where they spend their time and how you can influence their behaviour.