If they don't let you fly both I'd say fly the Hawker. Why would you want to fly an aircraft without ailerons? Don't do it. Fly the Hawker. Of course new Beechjets are Hawkers. I guess you're going to be flying a Hawker regardless of which one you choose.
If it is an old Hawker 400 I'd choose the Beechjet. If it is any other Hawker choose that over the Beechjet.
At least you had a choice. Now you just have to live with your choice.