I am assuming that you are, in effect, abandoning the old domain whether the old domain disappears or not, I am assuming that you prefer the new domain over the old domain. I am working with this assumption.
I am always in favor of taking a bit of pain to create a clean site/scenario. Otherwise you end up with compromises that complicate things for the future.
Having said that, and since you have access to change the inbound links of importance, I would recommend changing the links to point to the new domain and take advantage of your most important keywords to help focus and vary the use of your keywords.
Here is what I mean. Take 2-3 of your most important keywords for your site and use them within the link text. Also take 2-3 of your most important keywords for each page you link to and also use them within the link text. It may be that these are the same if your links all point to the same page. If at all possible, create links to various pages on your site. Vary the links to use the most important keywords for each page (not forgetting the site keywords). This does three things; one- it passes juice to several pages, two- it helps to create importance for your site, and three- it expands the keywords that can drive traffic. Because Google (at least) views a sites importance by how it is linked to, home page only vs. deep links and keywords used, the opportunity to link to other pages helps drive Google's view of importance. Something to consider.
While 301 redirects can pass link juice, there is a 10-15% loss in the process. As well, a link to the older site vs. the new site, does little to support the new site in the future. If you decide to delete the old domain, you will still have to redo the links anyway, so why not get it over with?
Sometimes, the best advice is to take any pain now and get it over with if it is better for the future, makes a cleaner site, and makes a better and more manageable scenario. Based upon how I read your question, I recommend to take the pain now and if at all possible expand how you link to your future site. You have a unique opportunity that not many people see everyday. You should take advantage of it if you could.