Mission do generally tend to have a "house sound" which is a bit like that. Some love it, while others are not so keen.
That said however, the speakers are just one part of the chain - if you also use a source and amp with similar characteristics, then the cumulative effect may be " not nice"
There are several problems with trying to advise on issues like this.
Nobody else has actually heard your system, hence it's difficult to even guess at the source of your issues.
You may be right in that it could well be your speakers, but equally it could be several other things too, or even all of them combined.
It's often a case of using one piece of equipment to mask the deficiencies of another. Not great, granted, but unless you have budget for a total system upgrade, there's little else you can do, given that you dislike the sound you have at the moment.
As the speakers are at the end of the chain, most people start with those, in the hope that they can use a certain model which can hide/mask (the speakers can't really correct them) these problems.
You may drop lucky, but it's really a bit of a hit&miss affair, often trading one set of issues for another.
There is always the "heresy"
of the treble control as well - not usually recomended, but given that you simply aren't happy with the sound at the moment..... well you never know!
If you have a limited budget and are handy with a soldering iron, you may be able to "tweak" the sound of your current speakers, or at least tame the treble excesses a bit.
Be warned at the outset though, that this can also be a bit of a hit and miss affair - luckily it's fairly cheap to do though - and while it may offer some improvments, what it can't do really, is give huge increases in sound quality - it's a tweak, not a wholesale sound transformation. It also requires at least some knowledge of crossover design before you start.
In fact, if the speakers are biwirable (I think they are), you could try placing a resistor (use a power unit, at least 10W I'd suggest) onto the HF+ terminal and connecting the HF+ speaker wire to the other end of the resistor - you'd have to try different values - I'd suggest starting at 4ohms or so. Basically this will reduce the level of the signal to the tweeter, and will alter the "balance" of the sound. The advantage is that it really requires no real crossover knowledge and needs no internal intrusion onto the speakers (hence no warranty issues etc).
If the speakers aren't actually biwired, just replace the "LF+ to HF+ links" with a resistor (don't do it to the negative terminals - leave them as they are), and ensure that the speaker cable is connected to the LF terminals, NOT the HF ones.
Otherwise, it's probably a speaker swap for a smoother sounding set. Try Tannoy, Wharfedale or Yamaha - but whatever, you really need to listen to them on your system in your room so that you can judge whether they will offer what you want (ie don't take my word for it).
Possibly also a receiver and DVD/CD player upgrade.