I currently use both because I have one through work. And yeah, they both have downfalls and are both corporations out trying to make as much $$$ as possible. When you sign up for service, they pretty much have you for 2 years unless you pay to break the contract. Both have occasional dropped calls, the very infrequent occasion where it seems like the network is down, and stores where it seems like you wait 30 minutes and if you've done any research know more than the sales rep you talk to.
But I would prefer alltel to Verizon for a couple reasons. One reason is better plans. If you compare plans side by side, for the price alltel offers more anytime minutes for the price, as well as the My Circle for unlimited calling to a set number of people not on alltel. I would also rate alltel's customer service a little ahead of Verizon's in my usage. Neither one is perfect nor ever willing to admit they made a mistake. Both will generally listen to you and try to help out. Alltel seems to have a shorter wait time for me over the phone. In the local store I always ask for the same person, he gets all the commission off the things I buy and has frequently really helped out in approving phone exchanges via warranty and even replacing a couple phones on the spot. Verizon also cripples their phone much more restrictively if you plan on bluetoothing your phone to your pc for mp3 files. Verizon does have the upper hand in several categories too though. They're a larger corporation so they get more exclusive phones that nobody else carries. Both providers generally have decent coverage (compared to others). In the JD Powers and Consumer Reports surveys that come out annually, in most cities alltel and Verizon are at the top of the list.
2008 Wireless Call Quality Performance Study - Volume 1 | J.D. Power and Associates (http://www.jdpower.com/corporate/news/releases/pressrelease.aspx?ID=2008037 - broken link)
Verizon Wireless, Alltel tops in Consumer Reports survey - RCR Wireless News
Verizon advertises a lot more about having 'the network' but it's not uncommon to see alltel ranked better in a few more places. But I think this advertising leads to more of a public perception that Verizon's coverage can't be touched anywhere in the nation by anybody, though that's often not the case. All in all, coverage is probably a scratch unless you're in a hard to cover area where one just happens to be far better, so in general I would go with the one with the best plan for your needs unless there's a provider that just has the phone you have to have.