Sure, both Congress and state houses are bicameral. They have two chambers. However, six cases argued in the Supreme Court in 1963 and 1964, collectively known as the Reapportionment Cases, decided that states could not justify apportioning representation in their state senates on the same basis as the United States Senate.
Secondly, the rules by which Congress legislates bear only a passing resemblance to those in state houses. Although the Constitution carefully limits the powers of each Branch of government, including Congress, it allows them to make up their own rules. Indeed, both chambers, the Senate and the House, operate under very different sets of legislative rules and processes.
This is why arguments that professional politicians who have served in a state legislature have some practical advantage over those who have not have no basis.
Even though I have walked the halls of Congress and the White House helping the President and members of Congress crafting and overseeing legislation affecting the military, and have had some experience in these matters, I have been doing my homework to be better prepared to represent you. Most importantly, I don't want to make any promises I can't keep because I failed to understand the duties and powers that I would have if you elect me.
Do you think my opponents are doing the same? I haven't heard any mention of it, have you?
The complete series of videos describing the legislative process can be found at Congress.gov.