I have an open day to do a day trip from Paris. Which would you pick? Loire or Chartre.
I understand they are approx. the same distance from Paris.
Which one will be easier to do without joining a tour group ( on our own, no rental car)

Chartres is the obvious choice since it has its own convenient train station and is essentially a single site.

Given your specific requirements, Chartres would be "easier" since it is pretty much self-contained, you don;t need a car to get around or to the main "attraction" there.

Chartres is a fascinating town to explore after viewing the cathedral and would give you a lovely days outing.
I have caught the TGV to Tours where we were collected by mini-bus to Azay-le-Rideau (has a fabulous Chateau)for the start of our week long Loire Valley Walking Tour.
Tours is big place and also has a magnificent cathedral.
If you're thinking about seeing a chateau you would have to hire a car or take a bus tour from there. You would be pressed for time trying to see too much.
Hope someone can advise better!

Chartes is a excellent choice for a daytrip. It's an easy train ride from Montparnasse station.

Woody

I agree that Chartres is the logical choice for a day trip. The cathedral and the town can be enjoyed in a single day.
The Loire Valley, OTOH, requires several days in the very least.

Chartres.

Agree on Chartres for a day trip - one big sight and a pretty town to explore.

Doing a small part of the Loire as a day trip would be exhasuting and frustrtating - in terms of what you would miss. To really do the Loire at all you need at least 3/4 days.

Ca y'est - Chartres. End of discussion.

Chartre. It is a nice town, has a so beautiful cathedral, is closer to Paris and leave you free time to enjoy the day trip.

I'd certainly put Chartres first. But if you want to see a bit of the Loire Valley you could take a train to Angers and visit the impressive château and the old town. You could also visit the magnificent Apocalypse tapestries adjacent to the château.