Old vs new Thundercats, which one is better?

Hard to say. It's really two different stories. The "first" Thundercats were visitors from another planet called Thundera actually seeking haven in a planet they called Third planet that was, for all the evidence provided, an alternate version of our Earth (Excalibur for example exists there) sometime in a distant future where mankind doesn´t exist or has departed to other worlds. Thundera has been destroyed by some malign intervention later revealed to be the action of a powerful and evil sword that had been kept inside the planet. A neighboring planet called Plundarr is home to a race that hates all Thunderians for no apparent reason whatsoever and they are called the Mutants that are actually alien antropomorphs that for some reason none of them resembles cats (you see, the Thundercats were created by a cat person). The only survivors from the destruction of this tragedy is a group of catlike humanoid warriors called the Thundercats who are led by their brave leader, Lion-O, also the wielder of the fabled and mighty Sword of Omens, the greatest weapon the Thundercats have. Unknown to the Thundercats who build a new base somewhere in the Third planet there´s an ancient and all-powerful evil entity in the Third planetcalled Mumm-Ra that sees the Thundercats as a threat and thus engages in accomplishing their destruction. Along the series we see the Thundercats defeat Mumm-Ra and the Mutants plus several other opponents and finally, with the help of other powerful relics from Thunderian past they manage to rebuild Thundera so by the end of the series the Thundercats defend now two planets.

Now think of the "new" Thundercats as "The Thundercats meet The Lord of the Rings" for Thundera is now a medieval kingdom in the Third planet where it has tall walls that prevent their reptilian enemies to enter their walled city. Most of the elements are there with  a younger Lion-o and a still alive Lion-O´s father. Besides those, there are some positive things such as the fact that the characters are no longer flat but round and have more elaborate motivations and their relationships are also more complex, in some cases entirely new. The kingdom is one day besieged and later taken over by a conjuction of several Thundercats´enemies working together to set a trap for the Thundercats who have to flee in a mission to retrieve the ancient relic that will free and help re-establish their nation.

In sum, the new Thundercats is worth a try, but still in my heart there´s nothing like the old series.