I hate to say this.. But both! When getting the ball rolling on a start-up, you want to attack all possible marketing outlets. Now, if budget is the bottleneck then I would consider running some analysis on your target audience and see if your users for your service will most likely be using Google to find you (SEO) or will they be more commonly found on Facebook (Facebook ads). You can open a Facebook page for your business and watch it's activity and traffic (analytics).. Take that analysis and then compare it to what your website sees through Google Analytics. This should tell you early on how people are finding your services, in return you will know where to put your money.
They both have their merit. It's often not about choosing one over the other but about employing multiple online marketing efforts simultaneously. As you start seeing the results you can begin to invest more heavily into areas that are producing better ROI.
This question cannot be answered before understanding or developing the following:
• Your brand strategy ( value proposition, positioning, messaging platform, etc.)
• Your specific area in professional services
• Your audience profiles
I believe even though marketing is strategic in nature, it is often tactical (what to do). First figure out who you are or who you want to be and then develop a marketing strategy to put your brand into measurable actions.
As others have stated, it depends. This jumps way into the tactical side of the answer, but I've had good luck running Facebook ads to custom audiences. But those campaigns were focused on attracting prospects at the top of the buying funnel rather than the people who are actively in the market for the service.
The effectiveness of the marketing channel will depend on the approach. If you're only looking to reach people who are actively looking for your service, SEO and Search Ads would be the most likely play.
If you want to build awareness, attract more leads, and work those leads through the sales process, then a more elaborate strategy leveraging content, SEO, social media, and advertising should be considered.
Facebook page / ads (more appropriately SMM) *and* SEO should go hand in hand. There are many SEO tactics that are inherently unused and even unexploited in general.
When you go for online marketing, remember that it is not a process that you would out source it to a firm and forget about it till they get you results. It is called a campaign because it *is* one. Treating it as such will help you in areas that you had not previously thought of. In all mentions of your brand online, think of how it would affect your SEO. Hire online and optimize the job posts for SEO; when you post a job on a popular platform, a multitude of job sites copy your ads from different job platforms and these repeated mentions of your company improve your online visibility and website ranking, dont go for blog posts about you - go for news posts; news articles that even barely mention you give you great credibility and is a better way to spend your influence and money as opposed to ads and most of all when you get 8-10 news reports about you, go for a wikipedia page; wikipedia ranks in the world's top websites, it improves your visibility and SEO in ways no social media effort can.
Google's knowledge graph on the right panel that appears in searches is something even more visible than the search results. Optimize that. Google picks it up from your social media and wikipedia pages and if you dont have them properly set up, it wont show a knowledge graph for you, or worse, may show one about some one else with a similar name when you are searched up.