To the OP:
The Callaway game improvement irons that you're playing are a full club longer than your Muira's because they are game improvement clubs. These clubs have lighter shafts, increased MOI (perimeter weighting), and decreased lofts... all things that help the average golfer hit the ball straighter and farther. They are also manufactured using casting process, which, truly has no bearing on feel.
The x-forged are good clubs, I liked the 2009s the best. The new 2013s are nice too, but I'm not a PX fan and never hit one with a DG shaft. These clubs will have more traditional lofts and shaft weights. They will be easier to hit than your Muira's, but likely shorter in distance and harder to hit than your GI clubs. They will also feel different, due to the design of the head and the distribution of mass.
My suggestion would be to go see a club fitter and look at swing speed, shaft weights, ball speed, launch angle and spin. Get fit for clubs you can consistently hit a precise direction and a distance.
As for the forged/cast/feel debate... Shorty is correct. I'll digress without using the term 'buttery' for the betterment of the interweb community.
I was once told 'not to confuse correlation with causation' during a statistics course, and that saying directly applies here.
Forged Clubs
Typically, irons manufactured using a forging process are muscle-backs or players cavity-backs (small cavities). Therefore, these head designs will produce a different feel and ball flight based on their center of gravity and concentration of mass (MOI). These attributes are correlated with forged clubs because of the design of the head. These attribute are not caused by the manufacturing process.
Players clubs are forged because they can be easily bent to the loft/lie/bounce that better players require. Forging is more time intensive from a manufacturing and materials standpoint, which is where your cost comes from... in addition to needing to recoup R&D; costs over a lower sales volume.
Cast Clubs
Cast clubs are often designed with moderate to extreme perimeter weighting. It would be difficult to forge a club with a large cavity and highly-manipulated weight distribution... melted metal and a mold work much better here. It's also much easier to churn them out at high volume and low cost...like hotwheels. This is important because most amateur players don't want to pay $1,000 for a set of irons.
These clubs have a lower center of gravity, which produces higher trajectory and spin, so manufacturers also decreased loft to compensate... there is part of your added distance. When you move weight from the center to the bottom/perimeter of a club, the feel changes. These is less mass behind impact, and the feel off the face is a bit harsher. The more perimeter weighing, the thinner the face, the harsher the feel.
The Bottom Line
Comparing them side by side, the average Joe would say the forged club is softer. He might wax philosophically about how pure the shots feel, or how boring his ball flight is, thanks to those Japanese forgings... The enlightened golfer will smile and know that it's all physics.
And for what it's worth... I play very often and score reasonably well, and I have cast clubs in my bag. They feel pretty darn good, flight the ball decently, and let me have some good rounds on bad days. I've got forged blades in the garage if you'd like them.
delav