I would have to agree with Mr. Green about Klonopin. It is a longer lasting benzo and is usually prescribed more long term. Ativan is usually prescribed for shorter periods on an as needed basis. Just ensure that you work with your doctor when switiching medications.
Klonopin is a longer acting form of Benzo. What you were on was a fast acting Benzo. It would kick in straight away. Last a few hours. Wear off. Klonopin is a more steady form of medication. Mainly dozed out twice a day. It covers the full day. But it doesn't have the same quick kick in effect. It needs time to build up in your system before it will really start working. As for strengths. They are equal in strength. But you never said how long you were on the first medication for? If it was a long time and you just stopped it and started taken the Klonopin you may feel some withdrawls until the Klonopin kicks in. You are meant to step over one to the other. Ease one out while the other is building up in your system. ( If you used it for a long period of time, which it may appear as you had to up your doze yourself to get the same effect as when you first began taken it )