while i'm fairly certain that the equipment used imparts some kind of character on any recording, the only similarites i hear in the two clips you posted are totally stylistic w/ regard to the music itself.
that is to say, you can probably get in the ball park with the digital portastudio that you have. one hallmark of '60s-type music is that most of the sound happens at the source. if the band playing sounds like that in a room, most of the variables are going to come from amp settings, drum tunings, mic placement, etc. ... and of course the most important thing, the players. certain tape machines impart subtle characteristics, that, yes indeed, can sometimes contribute to the magic. but i'm not sure that's what we're hearing in these examples.
i don't record digitally at all, or appreciate much about it, and i do feel that my own music depends on tape. but it doesn't depend on budget. i was working with cassette 4-track for many years (and would do so again if i had to choose between cassette or digital), so i would recommend getting a cassette 4-track if you don't like your current rig. getting a 1/4" 4-track or 1/2" 8-track reel deck is about as affordable as you can get in open reel. A teac 3340 would suit your needs really well.
a tascam cassette 4-track can be had for really cheap. I personally like the Tascam Porta 5 (I got one on eBay for about $35) or the 414 model (a bit more, but not much).
good luck and let us know what it sounds like when you get something together.
donny
