sphynx, Google has done some algorithm changes over the past few months. Have you done any SEO work on your website before? If these methods are considered shady such as keyword stuffing, aggressive exact match anchor text link building, etc., your rankings might be negatively affected.
Of course, since you noticed another company ranking significantly better for many keywords, it might also be the fact that their SEO is doing a really good job.
How much you can do to combat this depends on how much time do you have to spend on SEO. Is SEO your main source of income all these while? If it is and you don't have the time, it's time to consider outsourcing the efforts.
Here's what a good SEO will focus on after all the Google algorithm change:
- Content marketing
- Local SEO
- On-site SEO audit
- Avoid spammy tactics (if you think a tactic is spammy and not creating any value for Internet users, it probably is spamming.)
A recommendation from a colleague or a competitor might be good but it might also be that because all the rest are doing bad SEO, an average SEO effort is enough for them to do well too.

Good luck!
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