The White House - the residence of the US President - and the Capitol Building - the home of Congress - are two of the most secure buildings in Washington DC that allow for public viewings and tours. Of course, they aren't strongholds like the CIA headquarters of other top secret government buildings, but still have massive security features due to the extremely high profile politicians who frequent them. The question is, what's more secure?
Let's start with the White House. This was modeled on English country houses, and was open to the public until the early 20th century. The 'open house' informality of the White House was common in its early days, although during presidential inaugurations it would become quite rowdy. In recent decades, however, the security at the White House has become much more dense.
Tours, which were once much easier to book, took a short hiatus in the aftermath of the September 11th attacks. However, in 2003 they resumed on a more limited basis with groups who booked in advance. Serious background checks are now in place for visitors, and several areas around the compound are closed off to traffic. Around the grounds there are a plethora of cameras, guards, and even snipers guarding the roof (depending on the situation). The Secret Service and the US Park Police both provide protection, while the airspace around the building is strictly prohibited and protected by the Norwegian Advanced Surface to Air Missile System (NASAMS). Of course, maximum security is more intense when the President it around, and various areas of the compound are completely off-limits to unauthorized personnel.
So, how about the Capitol Building? Well, the home of Congress has seen its share of drama over the years, with presidential assassination attempts and bombings all having occurred. However, it is since the attacks of 9/11 that the building has seen significant security changes. The roads and grounds have been redeveloped, vehicle checkpoints have been installed at specific locations, and a section of a particular street has been indefinitely closed.
On the roads around Independence and Constitution Avenues, barricades have been installed that can be raised up when needed in emergency situations. All visitors are screened by both an x-ray device and a magnetometer, while in both of the chambers there are gas marks beneath the chairs for emergency use by the members. Security is also very high throughout, and in particular on days when Congress is in session.
One of the recent features of the Capitol Building is its Visitor Center. This subterranean, 3 level structure opened in December 2008, and is intended to bring all visitors into the building through a single maximum security checkpoint. This not only improves security and makes it more of a 'bottleneck', but it provides a variety of other features such as food courts, restrooms, and exhibits for guests. This new structure was largely brought on by the killing of 2 Police Officers at the Capitol Building in 1998.
So, as you can see, both the White House and the Capitol Building provide maximum security. Visitors are screened at both, security guard numbers are high, cameras are positioned everywhere, and various entry points are blocked off. In general, however, tours and access to the Capitol Building is probably slightly easier than the White House.