I'm not generally big on Ashkenazy, but his first recording of Rachmaninov's 2nd Concerto with Kondrashin is among the most beautiful recordings of anything...a ravishing tone, a great interpretation. It is far more representative of Ashkenazy's strengths then the recordings with Haitink and Previn. I love either Richter recording for a more menacing approach. I've a sentimental connection with the Rubinstein that benefits from the amazing Chicago Symphony/Reiner (been with me since youth).
The Tchaikovsky is not one of my favorite pieces. I like it most when it's abused, as is with the previously mentioned live Szell/Horowitz paring (if you can find it!). Szell brings the New York Philharmonic to a breaking point, a whirlwind of intensity...and Horowitz is involved!

Also I like a certain "boom chick" which rides high in a live Rubinstein performance with Dmitri Mitropoulos (if you don't know this fantastic conductor, Mitropoulos often conducted Prokofiev's 3rd Concerto from the piano! That's all you need to know

) If Richter, then Richter live. The studio account with Karajan came up dry (I think the two never enjoyed working together). There are excellent live accounts, though...with Ancerl, with Mravinsky, ect.
I am writing to much.
If picking one for each, with a gun to my head...
Rach: Ashkenazy/Kondrashin
Tchaik: err...Richter/Mravinsky