Both the destinations have their own enlightened beauty. But my piece of advice would we cover Gangtok and Darjeeling!! But my piece of advice would be to travel Gangtok first as there is unavailability of airport, the nearest route is to grab a taxi from Bagdogra airport. Believe me the thrill you experience on the road to Gangtok is like heaven.Small roads, lush green mountains on side, fresh water flowing, natures beauty at its best. Enjoy the glacial Tsomgo Lake which is s located at an altitude of 3,780 meters above sea level. It is also called as Changu Lake and is crossed by the Nathu la Pass on the north. Its a beauty catch to your eye. During winters this lake is at its best. Ahead on the route theres also a tourist attractions Baba mandir. During heavy snowfall this route to Baba mandir is closed usually. Later you can visit Hanuman tok and in evening enjoy the walk to MG Road After this take a ride to Darjeeling, on the way you will see the famous tea gardens, and sceneric lush green beauty The most important visit to Darjeeling is Tiger Hill. Wake up early this morning and start driving towards the famous Tiger Hill (11 km) to experience a sunrise like never before.Tiger Hill is famous to offer a panoramic view of Mount Everest and Mount Kanchenjunga together. As the first rays of the sun hit the place, you get to see the twin peaks of Kanchenjunga painted in shade of orange. Later you can plan for Guwahati, Shillong and Cherapunjee!!
I think climate wise Sikkim is better. As there is always a possibilty of rain in Meghalaya during that time.But if you can handle the rain Meghalaya is more beautiful option. Sikkim is altitude wise on higher side obviously. But if you want to enjoy hilly greenery then Meghalaya seems best.