IMHO,
Sounds like you've got clocking issue with the rme. Are you monitoring playback with external clock/sync?

That black box is good but only works in 16-bit :-)

I would look for some other issues. I use several of the RME Multiface, (they are replacing some M-Audio delta 1010) and they sound great. To upgrade I would start looking at Benchmark or Apogee.

Since you did not discribe the signal chain let me ask some basic questions.

Are you getting nice hot signal levels. If your levels are to low, you are wasting bits.

Is there an impendence mismatch?

Are you running balanced interconnects?

i used to run once, a spdif over a da-20 mk2, and was rather surprised about the ad/da's in the tascam they are fine, if you have one, it's ok to use it that way, but if you have to spend money, save a little bit and go for yeah, benchmark or apogee... much better...
if you're not into mastering, you hardly want need a dat in our days...
so go for propper ad/da's

Thanks everyone for reply!

iq,
I think clock is not the problem. I have only one digital box and that one is multiface. Multiface is set to master and freq. is 44.1.

yknot,
my levels are hot and I use hi-quality short (2m) balanced cables.
I mix on Mackie CR1604, the original, not VLZ. Just for information, I find this box sound very very good. MUCH better than later VLZ series, and I find it even better than mackie 8-bus which I used to work with.

axel,
I have plans to invest in 8ch adda converter (probably lucid) because I am not that satisfied with multiface converters. But I have to wait a little bit for finances...
I can get DA-20 really cheap. 50$ or something like that. Do you think it is a good investment to upgrade RME converters?

At the end...
After A/B-ing original mix with RME recording (24bit, 44.1) here is the conclusion...

The biggest difference comes from reverb. I use 3 reverbs, lexicon pcm70 for vocals, and 2x lexicon lxp1 for drums and other sounds.
In original mix, reverb is very 3D, and you do not actually hear it in the mix, you just feel it.
After recording, reverb comes very much in front, doesn't sound 3D at all and it is simply to loud and obvious.

The second difference comes from bass sound. I use juno106 analog synth, which sounds very warm and fat but after recording it looses a little bit of this character.

Third difference are drums. They are not so tight and punchy anymore.

With highs, the problem is not so big. But they are a little bit muddy. I can live with that.

in case of 50 bucks for a da-20 mk2 plus having a dat , go for it!
to tell how much better or if really better the ad . da's in the da-20 are, i would have to hear it, really, don't know the RME stuff so well..., just remember that i was surprised about the tascam ad/da sound, but it was long time ago...

i guess a real sonic step ahead you will have with propper ad/da's
for 50 bucks a dat, on the other hand i sold my da-20 mk2 really cheap, 'cause for my way of working dat became outdated...

hard to say really, try to make another a/b before you grab the da-20