There's more to it than cutaway or not.
First of all there's the matter of the cutaway. Does it effect sound or not? My own feeling is that if it does then it's not by much. Some years ago I spoke to luthier Nick Benjamin at the Lewes Guitar Festival. He told me that his tests show that the top is dead in the area where a cutaway usually goes. He thinks the back is still working just a little bit in that area, and so a traditional cutaway would not cost much in terms of tone.
"Dreadnought" is a specific shape. Martin guitars whose model designation begins with a D... are the classic dreadnoughts. Dreadnoughts are designed to be loud and to have a strong mid range.
There are other shapes. Here's my two flat tops
A Larrivee LV05 on the left, Morgan OMR on the right. Neither of them is a dreadnought. The Larrivee is a little curvier than a dread, the Morgan is a lot curvier. The Morgan is smaller than the Larry, or a dreadnought.
All sorts of things effect the tone. In no particular order...
- Body shape
- Woods
- Bracing
- Strings
- Saddle material
- nut material
- set up
- bridge pins
Both my flat tops have spruce tops. The Larry has mahogany back and sides. The Morgan has rosewood back and sides, and is also built heavier than the Larry. The Morgan has a lot more overtones and a generally darker, almost metallic tone. The Larry sounds woodier, has maybe a little more "sparkle" on the tops, and a bit more mid-range. IMO the mids are down to the body shape and the mahogany.
Strings.... different compounds offer different tones - though this may just be because for the same guage different compounds would have more mass. I use phosphor bronze 12s on both guitars. They have more mass than 80:20 bronze (the usual brass yellow compound). To my ears they have a little more clarity and discernibly more oomph. They also impose a little more strain on the guitar because of the extra mass.
OK... all of this is a bit vague, but understand that body shape and size, different woods, different strings can all effect tone.
What would be useful now is more information about your guitar. Model number? Woods? What's the saddle made from? What strings do you use and how old is the current set?
And here are the things that you can experiment with without incurring too much cost.
1) Saddle. If it's plastic then you can usually get a worthwhile improvement by replacing the plastic part with bone or one of the new specialist artificial materials like tusq. The nut effects things too, but not as much as the saddle.
2) Setup. Especially the way the strings break over the saddle. If the break angle is too shallow then you will loose tone.
3) Strings. Different brands, different guages, different materials. If you change guage or material then you may need to tweak the guitar. At the least you'll need to tweak the truss rod. A good setup will be better (but more expensive). Talk to your friendly local guitar tech and get some advice. If you go to a heavier guage than the factory ships the guitar with then you'll probably have to get the nut looked at. If you plan go heavier than the factory standard then maybe send the company an e-mail to see if the guitar will take the extra strain. 13s are no problem on either of my current flat tops. I used to have a Taylor Big Baby (nice guitar!) and the advice I got RE that guitar was to not go heavier than 12s.
4) Bridge pins - though the jury is out on wether you or your dog will hear the difference. Neil Young swears that they make a difference - he likes buffalo horn. Martin Carthy uses three regular pins and three brass pins. He believes that this makes a difference (he uses the brass pins on the high strings). But the saddle makes a bigger difference.
I don't believe you really hear your flat top when you play it. I always enjoy when somebody else plays one of my guitars because that's when I find out what they sound like. They sound OK when I'm behind them, but I don't get all the details in the sound.
