Competent and competitive are both used to characterize someone as at least adequately qualified or suitable for some role or position. Competent focuses more on the skill level itself, while competitive, in this sense, marks someone as attractive enough to be selected for (or "winning") some role or position.
having the necessary ability, knowledge, or skill to do something successfully.
"a highly competent surgeon"
As good as or better than others of a comparable nature:
a car industry competitive with any in the world
Competitive makes more explicit that such a situation involves a comparison between the person described and others in a contest for such a position or role, while this idea is implicit in competent (someone can't be sensibly considered good or good enough at something if no one, at least in theory, is not good or not good enough for that thing).
Should you upgrade or develop new skills that would make you more competitive in the job market?
--Baby Boomers and Their Parents
Both words can be used to indicate a relatively wide range of strength or degree of positive evaluation, but both of them generally indicate at least an acceptable degree of skill, capability, potential, or desirability. The dictionary I've cited here gives pretty good information on how competent can be graded as more or less positive. We tend to use very and highly to intensify both of these terms.
Competent is a useful word to know. It is one of the 7,500 most common words used in English. See the Macmillan Dictionary's entry for competent for more on this. Especially note that it is a red word there, and you can click What are red words? on the page for more information.
In some situations, competent can carry a negative connotation, as in He's not a great architect, or even a good one, but I suppose he's competent. In other words, it can communicate a just barely passable level of skill or ability.
Competent seems to be at a medium level of register (formality). In some very relaxed and informal conversations, it may be more appropriate to simply say something like she's a good/great lawyer.