Here is a quote from the Tascam website:
The 424mkIII is TASCAM's finest cassette four track. Its advanced feature set offers something for everyone. The 2 independent auxiliaries mean you can add two separate effects to the same channel... not something many of our competitors can do. The 3 band sweepable mid band EQ gives you the flexibility to focus on the sweet spot of the sound to help give it a little more life. The 4 XLR mic preamps keep your inputs quieter, and will save you from the hassles of finding the XLR to 1/4" transformers. The expert will appreciate these advanced features. The novice can grow into them, and improve their skills with time.
4 XLR mic preamps
6 channel strips & 1 stereo input
3 band EQ with sweepable mid on each channel
2 effect sends
3 3/4 ips high tape speed, and 1 7/8 ips normal speed
dbx noise reduction
Electronic transport for better tape handling
Individual track outputs
Separate I/O for mixdown deck connection & monitoring
Optional RC-30P punch-in pedal
And on the MKII:
For you or as a gift. The new 414mkII Portastudio is ideal for newcomers or those experienced in multitrack recording, packing high-end features into a convenient, compact and economical package. A high-speed transport, combined with Hi & Low EQ and dbx noise reduction means great sound. For convenience, there are also 2 XLR microphone inputs, and a 1/4" HiZ guitar input. Use it for demos, as a portable sketch pad, or for practicing recording techniques.
4 track recorder with 8 input mixer
4 mic/line input channels, 2 stereo inputs
2 XLR mic inputs
HiZ guitar input
2 effect sends
2 band EQ on each channel
3 3/4 ips high tape speed
dbx noise reduction
Optional RC-30P punch-in pedal
You can't go wrong with either machine, IMHO. The MKIII will give you a few more bells and whistles, and it costs more, but if you are serious about recording, that's the way to go. I found in my own experience that getting the cheapest I could find usually left me wishing I had more. There is sage advice that goes: buy cheap, buy twice.
As far as bouncing tracks, anytime you bounce an analog signal, you are basically re-recording tape to tape, and there will be signal loss. You can minimize it by making sure you have high quality tape in your machine, NOT METAL tapes, as they will act as sandpaper on your heads. Go for High Bias tape, not more than 60 minutes long. The longer tapes tend to be thinner and you will have problems with write-through and track bleeding.
One last thing, the MKIII has multiple inputs and decent pre amps, so you can record more than one track at a time and more than one instrument/vocal at a time.
Good luck, and I hope this was helpful.
Rokket