I think, it's hard to say whether you should invest only in FB ads or Google ads. The best approach would be, of course, to try both and see the real results. However, this approach will need some resources - your time and enough budget to spend on both platforms.
I would also look at your competitors, where they're advertising, check the CPC for the keywords you would optimize on Google Ads. Another great resource is the Facebook Ads Library - you can find your competitors and see the level of ads and ad copies they're using (creating nice ad images/videos and copies will also take some of your time).
Plus, it also depends if you've e.g. already set up Facebook Page, how active you're there, how many fans you have etc.
Last but not least, it's not always a good idea to rely only on one platform (maybe, you will find that only FB or Google works), however, there are also other marketing tactics you can consider, e.g. SEO.
The advantage Google Ads has over FB Ads is the intent of the customer. If you can put your products in front of them when they are searching for them they are more likely to buy rather than showing them a product while they're scrolling through their newsfeed.
Of course the success will depend on a lot of factors, like your product range, the demand for these products, your pricing, reputation etc.
Start by searching on Google for your products and see who's advertising and what your competition looks like. Set up a Google Ads account and use the keyword planner to find search volumes too and what you'll likely have to pay per click.
Then find your competitors' FB pages and go to the page transparency section to see if they're running ads. That's a great way to see what they're doing. If the ads have been running for some time there's a good chance they're working
Ultimately it's up to you whether you try one or the other or both, but if you do your research and learn how to do the ads properly you'll have the best chance of success.
Great question.. hopefully, I can answer this in a way you walk away with a way to take action.
First off, I would state FB or GAds, there is no which one is better. Both serve the same purpose (drive conversions/purchases), but can reach people in different aspects.
What do I mean?
FB Ads are almost always "disruptive". Think about yourself and how you scroll FB. When you head to FB are you intending to purchase anything? I would guess, no. With that you are very much so working on the FB Algorithm to find the best people to purchase your products.
Google Ads on the other hand are best used when people are actively looking for a product that you offer. These could be with Product Listing Ads (PLAs) or other methods - believe PLAs are still a viable option. Regardless of the method in which you use Google people should have the intent to purchase. The downfall with Google and Search is not everyone may be aware of your product(s) and looking to purchase it.
So what can you do?
Simply put.. try both.
If you are new to running paid ads, keep budgets small and almost always look to drive purchases as the goal for the ad campaign's objective. Even if you don't have any purchases from these ad networks... it is fine to try and build.
Another option / way to think about this?
Google Ads work best for products that may be higher price points as people are doing research. Thus they are evaluating what is best for them and going through a more typical buyers journey. If your product is a higher price point (really expensive pet products (talking hundreds of dollars) then Google may be best.
If your product(s) have a low price point.... FB and what is called "impulse" buying is an option. Imagine this being similar to when you go to a super market and the store has random smaller items at the cash register. You had no intent to purchase that pack of gum, but, because it is there, you did.
Hopefully this was helpful and opens you up to the world of Search Ads (Google/Bing) and Social Ads (FB/IG/etc)!
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What I suggest you before running any paid ads is optimizing your Shopify store SEO, here is a great article to starting out