In terms of marketing, no, you'll never be able to compete with eHarmony, they were one of the first online dating sites with a TV presence, they know how to sell their wares.
However, a one man show can absolutely out-react a large company like eHarmony. Assuming you've got the chops, you can push out new features and respond to user needs much quicker than a large development team can, simply by virtue of having no debate or discussion to get in your way.
So if you can get known, you can compete.
I had a similar idea to yours a little bit ago, but don't have the freedom of time to develop it. I extended the questionnaire system it to the business model, where the more questions answered and details provided by the employer, the cheaper it is for them to list. Take advantage of the high cost of posting on most job boards to drive for better matches. The idea being that large corporations would likely just pay the extra cost to get their opening out there, but small companies would be incentivised to provide more indexable data in order to get better matches.
Dunno if its something that fits into your idea, but I give it up simply because I'm sick of how awful all the job sites are.
A 1-person operation can do things that don't scale. When you read PG's story about Viaweb, their small operation played in their favor, because their customers would call up, and PG would solve their problem while they were on the phone with them. Customers love this kind of experience even more than not having any issues in the first place. One way to differentiate yourself is to offer this high level of customer service.
Also, large operations have higher overhead, and have to grow more quickly. This is usually at the expense of quality. Success for them may require $2M/year revenue or their division will be shut down. You may only need $200K/year to live quite comfortably. That means you can solve a small subset of the problem really, really well, and a lot of people will be very happy to use you because your product works every single time and you always answer their questions right away, and the other company just has a bunch of extra bells and whistles and upsells and annoying growth hacking stuff that gets in their way.