I have always had a philosophy when it comes to this and it is just my opinion. I look at every instrument as having it's own acoustic voice. The voice of the bass guitar comes from the combination of the woods used, their density, and the construction methods used, not the elctronics. In contrast, I look at pickups as the microphone being used to carry that voice. You can change pickups as many times as you want on the same instrument but if you don't like the acoustic properties inherent to that instrument chances are no degree of changing electronics is going to change that. As an example, I had 2 modulus basses at different points in time, the tone never worked for my ear which let me to conclude graphite necks are just not for me.
Think about it, if a singer is trying out for your band even if that singer is capable and has good technique, that does not mean the timbre of their voice is going to work with the music being played, and a new microphone is not going to change that.
Now, on the other side of that argument, if you have a bass and generally like the acoustic properties of the bass but feel it may be "slightly" lacking in a particular area, mids, bass etc. You can get a set of pickups that are more tuned to a particular range that can compliment and work in concert with the instruments natural voice, but no electronics are going to change the basses acoustic voice.
As others have said, consider looking into some different strings, new strings can have a surprisingly significant impact on tone. Steel v Nickle, Round v Flatwound, difference in gauge can all be very effective in tonal tweaks that might spare you the time and expense of changing pickups that in the end might not even achieve the desired result.
You need to ask yourself, is the sound of your bass almost there or way off, if you answered the latter, consider selling the instrument and looking for a new axe. Also if you're using a p bass, don't let this one turn you away from all of them, MIM P basses vary significantly in their acoustic properties and if you try 3 - 5 of them in a store chances are you will find one that works for you. Also if you do decide a new bass is the way to go, play the basses acoustically before plugging in. If it sounds good acoustically with no amp, chances are you will like what you hear through the amp.
Hope this helped.