Depends very much on what time of the year/month and how many days you have available.
I love them both but I would say there is more to see and do in the Upper Engadin valley than in Zermatt itself.
The Upper Engadin is a large, high alpine valley (valley floor is 1800m). There are many lovely small villages, lakes - on one, the Silsersee, there is even regular boat service in summer. You can make a day excursion to Tirano on the Bernina line or to Soglio in the val Bregaglia south of the Maloja pass. In summer many hotels there give their guests an Engadin card which provides free use of all public transport as far as Alp Grüm and even includes cable cars and funiculars. The golf courses at Samedan and Zuoz are challenging (for golfers anyway!).
Zermatt - beautiful alpine village with great restaurants etc and lovely views of the Matterhorn plus when you go up from there to the Gornergrat lovely views of the highest mountain in the country plus many others. If you are a hiker Zermatt is paradise. But once you are there - you stay up there until you leave. You do not have the variety of things to see and do that you have in the Engadin.
If you are taking the GEX spend 4 nights in the Engadin and 2 in Zermatt. That would be a good "balance" to me anyway. (I am from the Valais, the same canton as Zermatt, and I spend a week every summer in the Engadin. That about sums it up I think!)
My sister and I wanting to catch the Glazier Express to Zermatt for New Year, any suggestions on activities or sights or places to stay. We won't be skiing but would love to get to look around a bit and hopefully celebrate the new year with some locals.
Getting a hotel room in Zermatt for New Year's Eve only is almost impossible. Hotels, at that time of the year, expect and get reservations for a week at least. It is the highest of high seasons.
You could probably get a hotel room in Visp or Brig - 70 and 90 mns down the valley. But in Zermatt - I doubt it. Try anyway on www.zermatt.ch Enter date of stay and any available hotels will show up. Book now if you can.
I doubt you will meet any locals, but who knows? There will be plenty of people in the street - Bahnhofstrasse - to see the new year in.
You can book the Glacier Express (note - note "Glazier which means someone who puts glass in windows!) 90 days out and buy tickets 60 days out. www.glacierexpress.ch Seat reservation is essential. You cannot board the train without that.