If the mix doesn't sound good out of both systems then I'm afraid the mix is wrong altogether and will need fixing. Two different mixes might sound like a good solution but this is not the case; simply consider the range and variety of speaker systems out there and ask yourself whether you want to record a different mix for playback on each different setup. Reckon that'd be viable? Nope.
Focus on your monitors. They are the most accurate speakers you've got and if you get it to sound right out of them, it will most likely sound good out of your headphones too.
The goal should be consistency across all systems. The reason the track, through your headphones, sound amazing but not out of your monitors is because your headphones are giving you an innacurate idea of what is going on in the track whilst you produce; you are crafting the track to the headphones and not thinking about the other systems.
Consider using a spectral analyser on the master channel - this will give you a nice visual readout of the EQ curve.
Best advice is to take a reference song or two and run them clean through the spectral analyser - check out what the peaks look like. Now go back to your track and assess the differences between the professionally produced tracks and your own. The visual readout will help you immensely, I guarantee it.
This same A/B style of working with reference tracks is also really useful later on when you're mastering and want your tracks to be at the same level as pro tracks.
To summarise, some key production ideas to think about when trying to get good bass:
Make sure other higher pitch track elements have their low-end rolled off to avoid muddiness (where the track ends up as a bassy wash and you don't get any clarity.)
Steer clear of compression and other dynamics related inserts until the later stages of the track even if this means bringing the levels of all the other tracks down to even the mix.
Too much bass is just as bad as too little. This is so critical and so overlooked.
Hope that helps, good luck!