Those aren't particularly powerful monitors, especially in the low bass and high treble range, so it might simply be that they're not as good as your headphones.

Another, maybe more likely, possibility is that the volume is simply much more different between the two than it seems. Our ears hear differently at different loudness levels, and louder sounds with the same tone settings have much more bass & treble (punch & sparkle) at higher volume than lower.

To get speakers to be as loud as the level most people listen to headphones, the sound would almost have to shake the whole room.

someone recently asked me about what is better - headphones or monitors.  here was my response:

That's a very open-ended question unfortunately.  For instance, what if someone else is listening using the exact same headphones as you or the exact same monitors as you?  Then they'll hear it probably very similarly to how you're hearing it through those devices currently.  The real question is whether the headphones or the monitors more accurately represent the average listening experience for others, who will be using a wide variety of headphones and speakers.  You should record some stuff, then play it back on every system you have - car stereo, home stereo, tv speakers, cheap headphones, etc.  Get a feel for the sound on all of these devices, and keep asking yourself whether the monitors or the headphones better represent all those devices.

Headphones have an advantage over monitors in that they are consistent from one room to the next.  Monitors are not.  The size, shape, and wall/floor/ceiling material of your room will affect the tone.  Also, where you position the monitors in the room matters as well.  On the other hand, a room can make things sound better - the natural reverb adds a bit more space to the tone and things don't sound as dry.

The above point needs to be taken care of in your patches.  If you have absolutely no reverb of any kind in your patches, there will be an obvious difference in tone between headphones and speakers.  Keep in mind real mic'ed cabs, even when close mic'ed, capture some reverb from the room.  It may not be much, but it's enough to make the recorded sound be more similar sounding when listened to via headphones vs. speakers. So for my really dry rhythm guitar tracks, I tend to use at least a tad of E.R. in my patches.  Even if it's < 5%, it makes them sound more similar in headphones vs. speakers.  I tend to use dual cab patches for rhythm guitars.  For the darker cab/mic selection, I use more E.R.  For that channel the E.R. doesn't have the noticeable echo-y sound that can stick out too much.  I'll use between 12-20%.  For the brighter cab, I am more conservative, usually between 4-8%.  And I never use E.R. if I can use a Reverb effect instead.  Usually I simply don't have the DSP to do so.  If you do use reverb on a rhythm track where you don't want it to be too prominent, rather than exclusively messing with the decay and mix parameters, try setting the tone to darker/lower settings.  I usually set pre-delay to 0.

For me, I mainly use my headphones.  I can use them at louder volumes, and there's no room to consider.  I find they pretty accurately represent the majority of other playback devices I have.  When I follow the above advice about using a tad of reverb to prevent the tone from being too dry, they sound very similar to my monitors.

Now, there's occasionally some strange differences.  Really I'll hear something annoying about the tone in the headphones that I don't hear on the monitors or vice versa.  Once I hear it on one, I can pay attention and hear it on the other.

As for monitor settings, if you have EQ switches, I'd just play with them to try to get them to sound as flat as possible, which can be a difficult exercise.  I know my headphones are relatively flat, so I shoot to make the monitors sound as close as possible to the headphones.

So I'd say your headphones are probably gonna be the better representation, but your tone should sound good on both.  Don't rely on one totally over the other.  Test on both.  If a tone works one way but not the other, you may end having to compromise where the tone doesn't sound perfect on either but pretty good on both.  But you want it to sound best on whatever device most accurately represents as many other playback devices as possible.