In my experience, starting out testing one against the other is ideal (i.e. running campaigns on each and seeing which performs better).
It's also important to look at what your immediate and long term goals are for the spend. Are you trying to sell them something now, keep them engaged for a later release of a product, or some other action?
The key thing to note is that depending on what you're selling and what your keywords are, the bar can be a lot lower in terms of your bid per click if you go with Facebook Ads. Additionally: you can hyper target your audience with Facebook Ads like whoa (Google Ads are more limiting).
Ex: I ran both sets of ads for a new line of ballet inspired barre-wear (targetting both ballet dancers and barre students).
Both Facebook and Google Ads were linked to the sales page.
For Google Ads: I used keywords like "barre-wear" (low search volume) "ballet attire" "activewear" (limited relevance) and about 20 other related terms. The spend to results ratio here was underwhelming.
Keep in mind: I've only been working with Google Ads for a couple of years now. Better results are possible if you've got someone with 5+ years of experience who knows the system backwards and forwards, but for the most part, Google Ads are not DIY friendly if you want serious results.
For Facebook Ads, I did 2 campaigns:
1. Ballet Dancers: I targetted women in major cities (NY, Chicago, Atlanta, Los Angeles), who were under 26 and fans of ballet companies and schools in their city, and also those who were fans of major dance supply companies.
2. Barre Students: I targetted women nationwide who were between 26 and 52, married, above average household income, fans of barre studios in their area, fans of Lululemon Athletica (high end activewear brand), and did a couple of variations on different hobbies and activities to target specifically stay at home moms or wives who were active.
The results: $100 in ad spend // over 150 clicks to the product page // 20 new email newsletter signups // 3 immediate sales // 2 follow up sales within that week (so for a $100 product the ad yielded about $500 in sales that week from individuals who could be potential customers again (and 20 new people to market to for future sales).
