Hi - Be careful not to confuse "2 or 4 track" with "2 or 4 channel" The "tracks" are gaps (slots) in the recording head that actually provide a magnetic signal to the tape. The "channels" refers to the number of input/output signals the deck can handle. You can have a 4 track/2 channel machine OR a 4 track/4 channel machine - they are quite different.
I'll try to simplify the 2 track/4 track differences:
2 Track- Records in only one direction on the tape. You can't "flip" the tape and record the other side. The recording head "slots" are wider, thus using more of the tape to theoretically increase the amount of information recorded. And, since the "slots" are farther apart, the signal-to-noise ratio should be much better, with virtually no "cross-talk" or bleed through.
4 Track - Records in both directions, using 4 "slots" instead of two.
Recording time is doubled, since you can use both "sides" of the tape. But, since they are closer together, you will experience more cross-talk (one play head "hearing" the material recorded on another close-by head "slot".)
Adding to the confusion is the speed of the recording being made. The best would be a 2 track, 15 inch-per-second recording. The worst would be a 4 track, 3 3/4 IPS recording. Most pre-recorded tapes are 4 track, the good ones at 7 1/2 IPS, and the cheap ones at 3 3/4 IPS. Some pre-recorded 7 1/2 IPS tapes sound downright stunning, while virtually all 3 3/4 IPS tapes are pretty bad.
To sum up, if you plan to record live music at the best quality, a 2 track 15 IPS machine is your best bet. If you plan to play back pre-recorded tapes, a 4 track machine is a must. I would avoid any auto-reverse R2R decks, since they aren't usually very "Hi-Fi."
Fatparrot-You can play back 2 track on a 4 track machine, but track 2 (left channel) isn't properly aligned, so the sound isn't balanced - or very good, for that matter.
If you have any further questions, e-mail me & I'll try to help. I'm not a recording engineer by any means, but I've used virtually every type - and most every brand! - of reel-to-reel deck since about 1968, and will be glad to try to answer any specific questions you may have.
Best of luck,
Ed