Denver International Airport: There is no rail link to Keystone. The sensible car-free option is a prebooked shared mountain shuttle direct to Keystone lodging; allow roughly 2.5–3.5 hours, longer in snow or I-70 traffic, and expect about US$100–150 one way. A rental car is faster in clear weather (about 2–2.5 hours via I-70 and US 6) but is not a casual winter drive: reserve AWD/4WD with proper winter tires and expect chain-law and parking complications.
Eagle County Regional Airport: EGE is useful only when its limited flight schedule and usually higher fares work for you. A rental car is the practical transfer, about 1.5–2.25 hours via I-70 in good conditions; shuttle availability is much thinner than from DEN, so arrange it before booking the flight. Winter weather can erase the apparent time advantage.