Can't link back to them? Not sure what the problem could be unless you are trying to deep link and they have some sort of redirect to bump you back to the home page.
Links adventageous to your site? If they benefit your visitors. Working in the music business I see performers link to the venues where they are playing, venues link to performers' web sites. Both see it as adventageous to direct visitors to additional information. Links are adventageous where there is a real synergy rather than just trying to game the search engines.
yup that's what I thought well, the thing is, this other site is just plain not good and they are ahead of me on Google andit's disgusting, and I am trying like the dickens to get my rankings back and I don't know what to do