Are Claritin (loratadine) and zyrtec the same effectiveness when use for allergic rhinitis?

Yes. Claritin (loratadine) and zyrtec are both oral antihistamine agents that block the effects of histamine on what is called the h1 receptor. By doing this, they reduce the release of histamine, a substance that causes itching, runny nose, and sneezing. Zyrtec blocks the receptor a bit better, but the clinical effect of the medications is roughly the same. Zyrtec may cause some drowsiness, but may last longer.
Essentially. Uncomplicated allergic rhinitis responds well to both drugs. However, one study seemed to indicate that Cetirizine (zyrtec) works better. J allergy clin immunol. 1999 apr;103 (4):715.

Related Questions

I noticed allergies has 180 mg where as Claritin (loratadine) and Zyrtec says 10mg. Does this mean allergra is stronger?

Yes and no. The mg per se means nothing, it is the biologic or chemical activity that matters. For example, a ton of TNT will be far less powerful than a pound of uranium when used as an explosive. On the other hand, I personally believe that Allegra overall has a little more anti-histamine activity than Claritin (loratadine) but not necessarily Zyrtec.