250°F: the compromise
250°F splits the difference honestly. A 14 lb bird runs about 5 h 50 m at 25 minutes per pound — long enough to take real smoke, hot enough that the skin renders most of the way. If you have one smoker, one bird, and no strong opinion about skin, this is the temperature to run.
It is also the most forgiving setting on a windy day. A pellet grill or offset that drifts twenty degrees either side of 250°F still lands in a sensible range, whereas the same drift at 225°F stretches the cook past the point where the breast stays juicy.
At 14 lb you are at the ceiling of what should go on a smoker. Beyond this, the bird spends too long between 40°F and 140°F deep at the bone — the reason this site never recommends a larger one. Feeding more people means more birds, not a bigger bird, and two 14 lb turkeys will finish sooner than one 28 lb monster ever could.
How many people does a 14 lb turkey feed?
A whole bird is only about 40% servable meat once the bone, skin and carcass are accounted for, so a 14 lb turkey gives you roughly 5.6 lbs on the platter — about 11 adults at a half pound each, less if the table is loaded with sides and more if you are counting on sandwiches the next day. Cooking for around 10? The turkey for 10 people page does the shopping maths, and the portion calculator handles kids, sides and leftovers.