My experience is that if it's been over 4 weeks since your interview, the chances you will get a job offer are diminishing.

But it's all about negotiation. Call them up and tell them your situation, and like someone else said, tell them you are about to take another job offer. If they really want you, you will either get someone on the line right away or a swift call back. If not, then they're not all that concerned and I would just take the first job offer.

And if you don't have to sign a non-compete, then no worries - if you take the job with the first company, and two weeks later the second calls and offers, you can always jump ship. You will make some enemies if you do so, but it's always an option.