If you use good anchor text, then it will not affect your relevance. Anchor text counts towards textual content % and toward your relevancy %.
--Melanie
Jan there are a few things to consider. First if your sites are honestly on related topics then there's nothing wrong with linking more often between them. If visitors to one site would be likely to be interested in the others then it makes sense to link the sites.
If the sites aren't related say one is a site on auto repair and the other is on basket weaving then it really doesn't make sense to link them. Search engines (at least Google) will probably see the link more as an attempt at manipulation than they will as a genuine and honest vote.
I'm guessing your sites are related though.
Sitewide links will only have so much benefit. Think of it the way the electoral college works in electing U.S. presidents. Wyoming doesn't have a lot of people and so only has so many electoral votes. (I'm guessing 6, but I really don't know the exact amount) It's possible that all the people in the state vote for one candidate, but the state only gets those 6? votes.
Your sitewide link in the footer won't be seen as a thousand new links pointing to the other site. The value of each additional link after the first one probably quickly approaches zero.
That doesn't mean you should add the link. Again if real people are interested you've just given them a lot of new opportunities to find the other site.
You probably won't see a huge benefit when it comes to the search engines and where you rank though.
Of course it's very easy to find out exactly what will happen. Add the link in the footer and see what happens. If it looks like the link is hurting your traffic remove it.
My guess though is that it won't have large benefits and it won't cause major problems, but it both depend a little on the rest of your link profile for the site.