Having worked on Capitol Hill, I am of course particularly interested in this, and even more so because I've worked in both of those buildings. Moreover, in both cases I was in a first floor office very near to a public entrance. My first office in the Dirksen building was, in fact, literally next to an entrance to the building. That entrance was, as are all entrances to Senate and House office buildings and the Capitol, guarded by a minimum of two Capitol Police officers, and everyone who entered the building had to walk through a magnetometer and place their bags in an x-ray machine -- even if you were entering from one of the underground tunnels connecting the office buildings with the Capitol! -- so I always felt more than adequately protected.
Nevertheless, a security checkpoint isn't necessarily any guarantee that an armed lunatic won't try to get inside and start shooting up the joint. That was made adequately clear just a few months after I left the Senate for the private sector, when someone walked into the Capitol via the Document Door entrance and started shooting, killing two Capitol Police offices, Jacob Chestnut and John Gibson, and wounding another officer and a tourist.
There is, perhaps, a certain irony in that the first and only fatal shooting on Capitol grounds happened when it did; just three years earlier, security surrounding the Capitol had been massively increased following the bombing of the Alfred P. Murrah Federal Building in Oklahoma City. Not everyone was thrilled about the security upgrades -- Senator Rod Grams of Minnesota complained, "this gleaming 'jewel on the hill' is ever so slowly being transformed into Alcatraz on the Potomac" -- but personally I had no problem with it. At the time of the Oklahoma City bombing, Sen. Wellstone's suite of offices was located on the seventh and eighth floors of the Hart Building, and I can assure you that there is something supremely unnerving about watching news coverage of a bombing of a nine-story Federal office building from the eighth floor of a nine-story Federal office building.
Since then, security has, of course, increased even more, thanks to 9/11. But I working on Capitol Hill as a contractor on the House side from December 2001 through mid-2005, and I don't remember the security as being particularly onerous then either. Of course, my experience as a contractor with an official ID would have been very different from that of a visitor, which was the point Sen. Grams was trying to make in his Alcatraz on the Potomac speech. My sister made much the same point after she visited Washington DC trip this summer; she complained, not without cause, about the restrictions on what she could and could not have with her when she toured the Capitol, and about how little of the Capitol she was allowed to see, summing it all up with, "I think the Capitol should be much more open."
She's probably right. The Wisconsin Capitol is about as open as open can be. No x-ray machines, no magnetometers, no nothing. Heck, you can carry a concealed weapon in there, even in the visitors galleries of the legislative chambers. (In case you were doubting that the only part of the Constitution the modern Republican party cares about is the 2nd Amendment, I'll point out that while you can bring a loaded gun into the visitors gallery, you cannot display a signs, wear hats, or take photographs.) Granted, anything related to the Federal government, whether a building or a person, is a bigger symbolic target than a state office building or legislator. But it's also true that most Members of Congress take themselves very, very seriously, and with virtually unlimited resources at hand, it would be really easy for them to go overboard when it comes to their own personal safety.