I doubt that anybody is more fond of SXS's than I (equally, perhaps, but not more). I'm even considering throwing my colleagues a curve and shooting a SXS in International Trap competition this year, just for fun. But, even I am willing to admit an U/O is probably a better choice for clay sports.
SXS's are optimized for the field. They tend to be made as light as possible without sacrificing durability. This is an advantage when carrying all day and it's critical to achieving the lively handling and balance required for snap shooting wing shots. Field guns are also regulated slightly differently. Typically, they shoot flatter - that is to say, the pattern is more evenly distributed around the point of aim. SXS's should always be double triggered, to allow instant choke selection simply through pulling one trigger or the other (assuming they won't be used in competition).
U/O's are made both for the field and for clays competition. A good field grade U/O shouldn't be much different than a SXS (including the double triggers). An U/O for clays, on the other hand, is made to an entirely different purpose. High volume shooting over short periods of time require stronger, more durable actions. Competition guns are made heavier for this reason and also because the extra weight helps reduce felt recoil and shooter fatigue. The balance on a clays gun is usually slightly forward. This, along with the increased weight, promotes a smooth swing. The pattern on a competition gun is often higher against the point of aim than a field gun. This is so that a target shooter can see the target at all times (whereas shooting in the field we often cover the bird at the moment of firing). Single triggered guns are almost exclusively favored by target shooters. This allows for faster second shots when choke selection is pre-determined (you know your first shot will be closer than the second shot and you know the approximate range of both shots before calling for the bird).
The chokes best suited to skeet are very open chokes (IC, SK). The chokes suited to trap are much tighter (F, M). Skeet guns have shorter barrels (26 - 28"). Trap guns have longer barrels (30 - 32"). If you want to do your best in both sports, you pretty much need an average length barrel (say 28") and removable choke tubes.
So, IMO, you have a choice: Buy a new gun that will be better suited to the field and shoot it everywhere. Or, shoot what you have and save up for a while. When your savings approach the range where you'll soon be able to afford a clays gun, start keeping your eyes open for a good used gun that suits your criteria. Decent used competition guns run in the $1000 range.