I could be totally biased since I currently own a 2016 ILX but for me the Acura defiantly is better.
For one at least in the United States no one under 40+ years of age drives a Buick. I will admit the Regal and Cascada are good looking cars but the Verano is not one of them. The bulbous waterfall grill with the tacky hood vents and plain front end equal a car more likely to please former Buick owners than entry level premium buyers. The car could defiantly benefit from more sculpting like the Regal. The sides and back are even more plain but what really turns me off is the chrome strips on the taillights that look like eye lashes. Although you can get a turbo on the Verano it doesn't look sporty one bit.
The Verano Premium Turbo has an enticing base price of $28,670 in the states, but once you include the $890 driver confidence package (blind spot detection, rear traffic alert, lane departure, and forward collision) $495 navigation system, and $900 moon roof the car comes to $32,275 with destination. In comparison a 2016 ILX Tech Plus runs at $33,930 w/ destination. That's $1655 more for an Acura but that money is well spent since you get all the features found in the Verano plus a dual screen setup, Acura's navigation that has real time traffic alerts with rerouting, ELS 10 speakers versus Bose 9, Pandora and AHA capability, solar sensing climate control, and the biggest plus better residual value.
Performance wise both have a 0-60 in the 6.2 second range but the handling and shifts are much better in the ILX. Where the Verano shines is in the lack of cabin noise and space. In comparison the ILX is loud and the lack of extra room and extra 60/40 split hurt. Where Acura strikes back is the fuel efficiency where the ILX gets 25/36 and the Verano Turbo gets 21/30.
If we were comparing the 2013 ILX versus the Verano Turbo, the outcome might be different and would favor the Buick BUT I still think the Buick brand and styling is much more polarizing than Acura's and the residual value factor is a HUGE thing. Actually I just looked while posting and the Verano will be discontinued go forward at least in the States. check mate for the ILX?