Berlin to Prague car rental vs hire a driver?

We prefer to drive between Berlin and Prague (too much luggage to take the train)

Just another good reason to pack light. There are ECs between Prague and Berlin every two hours, and with advance purchase, they are extremely economical.

A car does not make sense in these cities - Prague has new mobile parking ticket system with camera checks - they can check up to 2,000 cars per hour.

Furthermore some rental car companies do not allow taking some car groups cross-border. If they allow it is expensive.

Also time of year can be an issue (winter).

As mentioned train is the better alternative: https://www.bahn.com

Berlin to Prague is ideal by train. To rent a car or even car with driver is a waste of money.

But as long as you are asking, take a look at My Day Trip.
https://mydaytrip.com/landing/berlin-to-prague

From the Daytrip website,

Each passenger is allowed to have one large luggage (29 x 21 x 11 inches) and one small luggage (22 x 14 x 9 inches).

If you have too much luggage to take the train, how is Daytrip going to help?

They, of course, will offer an upgraded car for more money. So be clear when you book, how much luggage, number of pieces and dimensions in cm. That way neither of you will be surprised.

With sufficient advance purchase, a Sparpreis ticket from the Bahn, for two people on the EC from Prague to Berlin, could be as low as 39,80€. Even a fully flexible ticket for two is only 143,60€. According to Daytrip, the trip with a driver starts at 225€. I think that is with the minimum luggage.

Best Trips don't have luggage limit please check out more info on
https://www.besttrips.tours/trips/product/to-prague/berlin-to-prague/

I really had to laugh at the Best Trips website (link above). One of the optional stops they offer between Berlin and Prague is the "Saxon Switzerland National Park".

So far, so good. It would be a good place to spend some time; I spent four nights there in 2012. But click on the information icon. It says "Swiss National Park - The only national park in Switzerland".

???

Who are these people and what do they really know about the areas they propose to take you to?

Sächsische Schweiz is one of many German national parks. It's located in Germany, east of Dresden, near the Polish and Czech borders. It's kind of a wooded combination of Zion and Bryce national parks in this country, with flat topped mesas and unusual rock formations. And they don't mention the two biggest sites in the Park, the Bastei, a bridge built out into one of the rock formations, and Königstein, an impressively impregnable fortress built on one of the mesas.