perhaps the circuit has two or more DC operating points, in other words the solutions are metastable states? One solution is a dcOp and the other starts from a dcOp and the voltage is swept - this can lead to different solutions. What kind of circuit is it? Have you tried using initial conditions rather than nodesets? I believe the former is a "suggested starting point" whereas the latter is more of a fixed quantity - if the nodeset values are not correct, this will force the simulation in a certain direction which may be why you arrive at a different solution?
Andrew will have more useful input I'm sure (and may even correct me if I'm wrong), but hopefully the above might be useful to you?
I'm not sure that the statement that a DC Sweep is a sweep (or set) of DCops is correct - I think that a sweep starts from a dcOp and then the parameter is swept, so this means that you could arrive at a different solution than a single dcOp - i.e. it picks "the wrong" metastable state for the operating point solution. IC's are used for transient simulations and a transient starts from a dcOp, so I assumed that IC's would apply, my apologies if this is incorrect, and also if I've got the nodeset vs. the IC mixed up! The fact that you need to use nodesets tells me that there has already been difficulty arriving at "the correct" solution, so this does indeed sound like a metastable state problem. Have you tried sweeping down from 1.1 to see if the solution is different? What can a transient simulation tell you?
what about a parametric sweep of dcOps?