Frankly, there is no one better than the other. Instead of asking which one is more profitable, the criteria should be based around these questions:
1.    Better fit for the budget
2.    Better fit for the landscape
3.    Stage of target buyers

Digital advertising budget and Acquisition costs:
Understand what you are going to sell and how much you can spend based on that. Don’t just spend recklessly, but by understanding your target audience. Maximize your process of retargeting first and then use your leftover funds for other funnels.
This will make sure you get the best returns & the customer journey.

The industry and its competition
Put your industry and its likely costs in the Google Keyword Planner. You need to have hundreds of impressions first, to know what keywords and budget system is working for you. When you have a tiny budget and an expensive click then it is advisable to focus on the landing costs too.
Here, Facebook Ads might prove profitable than Google Ads, because they have extremely powerful targeting capabilities in many industries.

Defining your objective:
Once you have seen your budget and affordability, the industry competition, so now it is the time to see what are your expectations from the market strategy.
As per your goal of brand awareness and demand generation, Facebook Ads are profitable. However, for the goals of lead and sales generation, Google Ads is good. Here, the user might be looking for what you’re selling, therefore, you would be targeting people with higher intent to purchase.  
You should measure quality and see what your cost per solid, qualified lead is.

Stage in a buyer’s journey:
It is a significant part to note where the buyer has reached in his journey, thus, both platforms are useful to track this information.
If you’re looking to capture users in the moment of their search for the product, then Google Ads is best for you. It has a high level of intent from the audience.
For getting more initial awareness or ongoing consideration, Facebook Ads could help in targeting those with unknown product needs.

Product maturity and overall Service volume:
If your company has some product/service that has no search volume then Google Ads cannot give you that volume. But there might be a series of keywords that your product address about your business. You need to take 10 times careful steps in this stage while choosing your Ads platform.
So, instead of targeting by user intent, you can target using demographics & interests too.

Brand Recognition:
A new company may look the increasing the awareness of their brand because instead of spending a lot of effort in SEO and Digital Marketing, their brand might not be searched in comparison to the already established brands.
When users see your ad ( a company that is non-recognizable for them) and your competitor’s ads (recognizable company), they are more likely to be driven towards your competitor. This is because they have higher clicks through rates and paid advertising.
For building your brand awareness, start with Facebook channels and other social media platforms, before jumping into Google Ads for success.