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I'd generally prefer the 34B vs the A-3440, because it's newer. You may get better size/weight comparison and lower noise specs with the 34B, also because it's newer, but in this game condition is everything and can vary a lot unit-to-unit. Parts would be more available for the 34B, but you may be on the second hand market for parts on both units. They're both considerably obsolete. Tascam Corp. would have simpler and more common parts for both. Complex and higher value parts you may be scratching dirt.
There is also the "std" Tascam 34, which is straight line level I/O, without the external mic inputs and onboard headphone monitor of the 34B. Based on these design upgrades, the 34B can be a little more versatile in the field, as is.
Is there any reason you want to go with 4-track vs 8? The Tascam 38 can give a boost in production value at a price boost on 1/2" tape, but the Fostex E-8 is a 1/4"-15ips-10.5" reel 8 track that might not be bad if you can find one in good condition. Keep in mind the narrow track width of 1/4"-8-track will also affect the fidelity specs, which is where 1/4"-4-track will trump it as a format.
4-tracks can be very limiting. I'd not suggest relying too much on track bouncing if you work alone, but working with a group 4-track can be satisfactory, or if you're ok with a very sparse production of your solo efforts.
There is also a Tascam ATR-60/4, which is a lot harder to find, but 4-tracks on 1/2" tape would sound HUGE, also with the price bump.
A good place to start might be a good condition 4-track cassette Portastudio, such as the Tascam 246, unless you're wedded to the idea of 10.5" reels at the outset.
With used equipment condition is everything.
