I'm not familiar with Quicken for NonProfits and I'm not an accountant, but I've completed the 990-EZ a couple of times. If you've kept decent records, it's not too bad, but I've never done the big 990, and I'm sure it's more complex.
The key to the 990-EZ is understanding how to classify your income and expenses for the year. When you've done the 990-EZ once, if you have good supporting paperwork, you should be able to do it next year in a jiffy. The classifications won't change from year to year. You might decide to restructure your budget categories to better match the requirements of the 990-EZ, making it even easier to prepare the form.
I looked at a different software product that claimed to support 990 preparation. All it had was a field for each category that gave you a place to record which line # on the 990 that particular category matched up with. You still had to understand the 990 well enough to know which line # to assign. It really wasn't much of a benefit. This was pretty unsophisticated software, and I would expect more from Quicken. But there's no way Quicken would know your fundraising expenses from your program expenses, so I gotta believe you still have to understand what the 990 requires, at least at a basic level.
If I were you, I'd take the 990 that your accountant prepared, plus any supporting paperwork given to the accountant in order for them to prepare the form. This would probably be an Itemized Categories report for the whole year if you're using regular Quicken. You should be able to trace the $$ from your report to the 990 so you can compare last year's 990 to this year's report. You should then be able to prepare this year's 990 fairly quickly. At minimum, it should take a lot less time from the accountant than it did last year (and thus cost less).
You can order a copy of the Form 990/990-EZ and its instructions, free of charge, from the IRS at 1-800-829-3676. Get a copy and read it over before you throw in the towel and hire a professional again or buy very expensive software. As far as Quicken Non-Profit goes, it would be nice to know if the additional features justify the expense. (note: I couldn't find info on the web about Quicken Non-Profit. Are you looking at Quickbooks Non-Profit?)