Defy defynately. Giants are brilliant bikes and brilliant value, and you get enough grease in all the places grease should be - bottom bracket for example. I know from personal experience that this doesn't always happen with Specialized bikes which are always built down to a price point..
I have had bad experiences with both, but to me the Giant was worse. Everybody has different experiences though I guess.
My Specialized Secteur Sport: Rear wheel constantly going out of true. Replaced wheels with Aksium's as I was fed up of it, and from what I have read cheap Alexrim wheels are just shite anyway.
Ex Wife's Giant hybrid: Can't remember the exact model, but whether it was down to me not checking or expecting better I do not know. I took our bikes on holiday only to find that the rear hub on the Giant was really loose and rough as hell when spinning the wheel with loads of play. The bike had done less than 150 miles. It was just to Center Parcs so she just used it, probably knackered the wheel totally. Whom this bike was aimed at should not be expected to be re-packing/adjusting cone bearings at under 100 miles, just IMVHO.
I posted threads on here about both bikes but was ages ago.
If my Secteur had the Mavic CXP22's like the later models appear to have I am sure I would have had no issues.
I have just come to the conclusion that entry level wheels are probably crap, or maybe I've just been unlucky. Certainly have no regrets buying a Specialized and if and when I can afford it I am positive my next bike would be a Roubaix.
Out of the 2 I would probably get the Giant because it is more relaxed, but then again I would rather have a Secteur. Maybe the OP should be looking at that bike instead of the Allez if they want a more relaxed geometry bike that is.