As a local who has used both stations on a daily basis over the past thirty years, I'd go with Zurich rather than Basel.
I know this is contrary to what several people have said, so here are my reasons:
- There are no ramps in Basel, so to change platforms in the Swiss part of the station, you will either have to take your luggage up a long staircase at one end or use the lift/escalator at the other end. So if you are at the wrong end of the train you may have to do some walking to get to the lift and on an international train you will most likely have to queue. And this may impact your ability to make your next connection.
- Many, if not all of the French trains leave from what used to be the old French station. That means in addition to what I described above, you'll have to get yourself from the Swiss part of the station to the old French part of the station.
- When I was there at Christmas time, I found the signage was poor, there was a lack of details on train arrival and departure and there were long queues for accessing the information desks. (See last paragraph about construction work)
By contrast in Zurich there are multiple points at which you can switch platforms using lifts, escalators and ramps, so much so that you will probably have to walk no more than say 70 meters to get to point where you can make your changes. And it is well signposted with plenty of information about train arrivals and departures.
You should be aware that there is major construction work going on in many train stations this year (including Basel) as an law requires all stations to be made more accessible for parents with buggies and people with disabilities. This means platforms are being raised/lowered and new low roller rolling stock is being introduced. This might have no impact on you or it may delay your trains, make it more difficult for you to switch trains or even find where trains are departing from. So check carefully before your travel in case anything has changed.