Then I believe they are just not hard pressed about the notice period thing since they know you are unemployed.

And you didn't happen to mention to them during the interviews that you can start asap ?

Pick the one that you think is better as a company and better for you to work for. Good Luck.

Thanks, I was honest about my situation with both companies. Probably you are correct and they would accept a mid-Spetember start date. I'll let you know how the situation develops.