i have the rockbass streamer as well. 4 string though. no diff in the pickup type or dimensions cos it's a 4/5 string model.
i know what it lacks. the pickups arent fantastic, they lack some definition and output.
changing pickups might help. so far the only exact model i've seen that replaces the dimensions of the stock pickup is the bartolini X44CBJS/CBJD pickups. there might be other similar ones but that you have to do your own research.
alternatively, like what i'm thinking of as well, is to add an onboard preamp. these are little electronics you put inside the guitar that would enhance your tone. they also feature on-the-fly eq-ing as some of your tone knobs on your bass would be able to control the bass/treble/mids. you then wouldnt need to lean over to your amp to modify the eq.
this would make your bass active. active basses have a battery in them, unlike passive ones. what makes them different in tone is the 'hi-fi' quality you get out of them. they have less noise, are cleaner and more present sounding.
passive basses (like ours) have no battery in them. they have a more 'vintage' tone and sound more 'loose'. i hope you get the picture.. (i mean.. sound =p)
you can find onbard preamps like Aguilar, EMG or even MEC ones. of course there are even almost unaffordable higher end ones like the U-retro or others.
also, another option is to get an outboard or floor preamp like the hartke bass attack (which i own) or a sansamp BDDI. these work rougly the same way as an onboard preamp except that they have more features like tube amp simulation. the hartke is relatively cheaper at abt $130 and performs its task quite well. the sansamp BDDI is more than twice the price and is in some ways, better.
you just have to do your own research like the man exin says. to see what suits your needs and preferences. hope i've been of some help.