I don't know about the Panther ammo, but I'll tell you what I know about the Tiger ammo.
All the info is taken from " Germany's Tiger tanks : Tiger I & II combat tactics " by Thomas L. Jentz.
Types of ammo: Pzgr.39 , Pzgr.40 , Gr.39 HL , Pzgr.39/43 , Pzgr.40/43 and Sprgr.
Pzgr ( Panzergrenade ), Gr ( grenade) and Sprgr ( Sprenggrenade )
The Pzgr.39 was armor piercing, capped, ballistic capped with explosive filler and tracer.
The Pzgr.40 was High velocity, sub-caliber, tungsten core with tracer ( the Tiger only carried a few of these for use against heavy armor like Stalin tanks )
The Gr.39 HL ( HEAT ) was based on the hollow charge principle, it was less accurate and less destructive than the Pzgr.39. It was used against armor and soft targets.
The Pzgr.39/43 is like the Pzgr.39 but with a bigger charge, the same goes for the Pzgr.40/43.
Shell weight and Initial velocity:
Pzgr.39 10.2 kg 773 m/s
Pzgr.40 7.3 kg 930 m/s
Gr.39 HL 7.65 kg 600 m/s
Pzgr.39/40 10.2 kg 1000 m/s
Pzgr.40/43 7.3 kg 1130 m/s
Pzgr.39/40 and Pzgr.40/43 was for the Tiger II only.
Pzgr.39 and Pzgr.40 was for the Tiger I only.
Gr.39 HL and Sprgr. had a different length for Tiger I & II.
Tiger I could open fire at stationary enemy tanks at ranges up to 2500 m.
Tiger II could open fire at stationary enemy tanks at ranges up to 4000 m.
At 2000 m the Pzgr.39 could penetrate 84mm of armor at an angle 30 degrees.
The Pzgr.40 could penetrate 110mm of armor at this range, the Pzgr. 39/40 132mm and the Pzgr.40/43 152mm.
There is alot more details in the book,but it would take up alot of space in this thread.
Hope this answers some of your questions.