Tape is a pretty different sound, you get rounded transients, uneven frequency response, and a lot of third harmonic. I used to work with professional Studer and Ampex machines, and I am a fan of that sound, though maybe for not all music. I do own the ATR-102 plugin, but haven't used it for a while. I think I like Studer A800 better.
Tubes are something different altogether, but the overlaps would be transformer stages. Ironically, you can make much cleaner signal paths with tubes than tape, and there is just something that can't be emulated about them. Esp when you here a really nice NOS tube, it has a 3D quality that just adding harmonics and EQ can't do.
I dont usually go in for tube amps though, because the ones I have used were slow, had poor channel separation, and rolled off the treble. I trust there are great ones out there, though, and tube preamps are definitely cool.
The player I use is my streamer, which doesn't have DSP.