How do you define depth?
Here is my attempt for both men and women: Ability to surrender heart, mind, body, and soul to the one he/she loves. This a two way street.
All the talk about intelligence, experience, money, and appearance are missing the mark. These are like pre-requisites. Depth seals the deal.
Intelligence and maturity could be different types of depth that could make life with someone easier, but how are these really different from wealth? The type I am thinking about is about the ability to be intimate.
Qualities that seem related to this:
1) comfortable and content with self.
3) not a whiner
4) no preoccupation with appearance
The 4 above can be summed up as "mature".
Women who know how to let a man be a man is a big plus, as is men who know how to be manly when given permission.
I could replace "not a whiner" with "ability to be fair". "Respectful" would also fall under "fair". "Whining" and "not fair" implies trying to get something material or emotional out of the other person without just cause or compensation. So someone in love with you is not showing depth if unconsciously trying to extract too much. Not being able to detect that you are being harmed by their actions or requests is a lack of "depth". Intelligence is thereby deeply connected to depth and maturity, but it is definitely not the key.
Many here have mentioned preoccupation with appearance. "Narcissism" usually has roots in unconscious low self-esteem that results from childhood traumas. It can appear confident, happy, intelligent, etc, and yet have absolutely no depth when it comes to romantic intimacy. A deep person can see "something is off" when trying to get to known a "narcissist". I don't like using the word because its an incredibly brutal accusation against someone who has had a serious injury in childhood, and there all levels of it including "normal" people. Above all, the pure narcissist's self esteem can't be threatened. The is a permanent road block to true intimacy. They can love, but not be loved. The internal person the narcissist might have been has often been killed off by childhood traumas, be it faulty/bad relationships (or lack thereof) with parents or whatever.
"Mature" is not a hardened type of maturity.
"Confident" is a key to attraction, maturity, and depth. But it is not a requirement for anything other than attraction. Someone with low self-esteem and conscious of it can have plenty of depth, even more than they realize. But I do not think they can or should end up with someone confident. Love is fair even if fairness does not lead to love.
The confident find the confident. The down-trodden find the down-trodden. If God is merciful, the shallow will stick will find the shallow.