A university email address that I had long used become unavailable in 2011, so I faced the decision of what to use for publications, and indeed what email addresses to use in other places.
My main criteria was that I wanted a permanent email address, and I wanted maximum control over the email address, including reducing the possibility that others are reading/storing my email, and the option to change my hosting if I was unhappy with it while not having to change my email. Changing email is a real drag, and I think it is a good idea to use a permanent address for publications if possible. If someone is contacting you regarding a paper, and it bounces, it is possible whoever it is will just give up. Your prospective correspondent may try to search for a more current address, but why make it difficult? If you have a common name, searching may be more difficult.
The main issue asked in the question is what is more professional. Personally, I think this is a minor issue. Maybe some journals care, but I don't see why they should. They should be more concerned, in my opinion, whether you will be contactable by this email long term. Unfortunately, in many cases it is not possible to update publication email addresses afterwards, even online, so that makes it doubly important. Email to my old address (which I stopped using in 2011) now bounces, which is unfortunate, but I can't do anything about it.
There are many choices available out there. They include:
1) Free corporate email addresses. Google's gmail is a popular example in this category.
PROS: They are free. It is permanent as long as the provider does not close up shop or close your account for some reason.
CONS: They are not university addresses.
Someone is probably going to read and possibly sell the contents of your email. Otherwise, why would they give away something free? Also, if the email hosting is hosted in the US, the NSA may store your email. As we know from recent news revelations, for gmail, we can assume that both Google and the NSA are going to be going through your email, or at least keeping it.
You have little or no control over the quality of the hosting. Even access may be problematic at times.
2) University address (possibly using alumni accounts)
PROS: University address, which is generally a good thing for academic publications. The NSA might still sniff through the email, but it is unlikely the university will, though who knows these days?
CONS: Little control over the quality of the hosting or other parameters like the amount of storage allowed. If you want to change to another host, you will have to change the email. Possibly not permanent (for non-alumni addresses). If you don't work at the university any more, they will probably eventually shut down that email address (again, for non-alumni addresses).
3) Create a custom email, including buying ones own domain, and paying for custom email hosting for email addresses of the form firstname.lastname@example.org.
PROS: Complete control over the email hosting. If you don't like the hosting, you can change it. One hopes a paid hosting company will not sniff through the email, though again who knows? For US hosts, the NSA is still a concern. It is a permanent address as long as you own the domain. You can make the email address easy to remember and to tell someone over the phone. Mine is extremely easy. Also, you can use email@example.com; i.e. you can choose whatever username you want.
CONS: Not a university address. You have to pay. However, the charge is not excessive; I pay $10.00 a month, and this is on the expensive side. There are cheaper options.
As you can guess, I went with option 3.