Offering a pilot perspective: one of the most hazardous things you can do in a transport aircraft is go to an aerodrome you've not landed at before (in over 50% of hull losses, one or both operating crew members are visiting the destination for the first time). Moreover, most (but not all) alternates are smaller airports than the destinations they serve, with shorter runways and less comprehensive facilities. Those factors would, in general, cause me to err towards landing on the 'blocked' runway. If it goes wrong, I can always steer off onto the grass. Giving me accurate information will be critical.
However, runway length, aircraft type, approach aids and weather will be critical. Say it's a 3,000 metre runway, a C525, with ILS and CAVOK, I'll press on for the blocked runway, knowing I'll use less than half of it. If it's an 1,800 metre runway, a Global, VOR approach in minimums, then it's a lot more risky and diverting will probably be better.
If this is an oral board question, may I also suggest that being very precise with terminology will stand you in good stead. A pilot can't 'declare a full emergency', thats the controller's job, based on a declaration of emergency (mayday) or urgency (pan pan) by the pilot. In this case, it's likely that 50% of power units on the biz-jet are u/s, which swings it to 'full emergency'. That said, one engine inoperative landings on modern aircraft are a non-event, and in fact, landing distances are usually not significantly lengthened (20% more perhaps, not 50%). Serious flap and brake problems (or the hydraulic problems they arise from) cause big increases in LDR, not engine trouble.
Finally, that 15 kt headwind is significant. During landing, kinetic energy is dissipated, and it's proportional to groundspeed, not airspeed, squared. So, considering this case non-dimensionally, touching down at 130 KIAS in still wind leaves (130 times 130=) 16,900 units to dissipate using reverse, brakes, etc. With a 15 kt headwind, it's (115 times 115=) 13,225, or only 78% of the energy. That's likely to make the whole thing a non-event - other than calling into question how the 737 got as far as the stop-end!