That question is quite hard to answer, since I don't know how to quantify the security breaches. You have to keep in mind that the Cold War lasted for more than four decades, involving dozens of countries.

For example, taking just one country - the UK, and from one source - Peter Wright, a former senior counter-intelligence officer for MI5:

(on the Communist Party of Great Britain) "Most of these covert members were not the same generation as the classical secret Communists of the 1930s, many of whom had been later recruited for espionage. These were people in the Labor Party, the trade union movement or the Civil Service, or some other branch of government work, who had gone underground largely as a result of the new vetting procedures brought in by the Attlee Government"

(Spycatcher, p.55)

However in the next page:

"Once MI5 was in possession of the PARTY PIECE material, the CPGB was never again in a position to seriously threaten the safety of the realm. From then on, MI5 was able to locate every single active Party member, particularly the covert ones, and monitor their activities, preventing them from obtaining access to classified material where the risk arose. The PARTY PIECE material was Y-Boxed, and remained of enormous assistance right up until the early 1970s..."

The book gives me the feeling that UK's counter-intelligence efforts were frequently hampered by bureaucratic inertia, as well as moles (e.g., the Cambridge Five, and also Wright's allegation that Roger Hollis - one of the Director-Generals of MI5 during his time in the agency - is a Soviet agent).

So to summarize:

a. how extensive was espionage in the Cold War? Very, by both all sides.

b. how compromised were our secrets? I don't know how to answer this; for example, VENONA intercepts show that the Soviets managed to obtain private telegrams sent by Churchill to Roosevelt / Truman (p. 182), and of course, secrets of the atomic bomb. But what is the "big picture" verdict? Well, between the capitalists and the communists, the former won.