Having flown the LR-60 and not the Hawker I can not make a very good comparison. The engines put out about the same amount of thrust, 4,600 lbs each, but the 60 is a Pratt and a full FADEC which, BTW and IMHO is very nice and quite reliable. The Hawker 800 has a TFE-731-?. Also, a very reliable and well known engine. The Hawker 1000 also uses the Pratt.
Where the LR-60 is weakest is in its brake energy. The wheels and brakes are little more than those on the LR-35. It has a lot of get-up-and-go, but because of break energy, high hot and heavy performance figures suffer. Still, on one engine at an altitude between say 15,000 and FL200, it can do 300 knots. I really enjoyed my time in this airplane and the time I spent teaching in it. However, I wouldn't mind getting to know the Hawker.
Remember though, the people riding in the back are the ones paying the bills and their comfort is paramount to whatever the crew would prefer. Lots to consider.