What dual core processor is equal to pentium 4 3.8ghz with HT?

You can't really compare a single core processor with a Dual or Quad core. They are all completely different in how they handle data. Also some software and games (older ones) would probably run better on a single core processor with a higher speed than a multi core processor running at a slower speed.

Newer games and software on the other hand, take advantage of multi-cores so even a modest 2.0ghz dual core could easily beat a single core.

Its a common misconception that people think having a 2.0ghz dual core means that is a 4.0ghz, or having a 2.2ghz Quad core means 8.8ghz. This is untrue, basically because of the reasoning I gave above.

A dual core has two complete processing units in a single casing, generally with independent level 1 and level 2 caches and a shared level 3 cache. By comparison, a hyperthreaded processor (with one core) appears as two logical processing units, with many resources shared between them. What a dual core, or hyperthreading, DOES NOT do, is double the speed. If something is not optimized for multithreading, then it can only occupy a single core (or thread of hyperthreading) at a time, though the presence of an extra core or thread can allow background tasks to proceed without taking anything away. Since pretty much any processor is at least dual or hyperthreaded thes days (even the Netbook ATOM N4xx series processor is hyperthreaded), then we can expect to see better usage of multithreading in future

Pretty much EVERY dual core processor beats a P4 3.8 GHz. Core 2 Duos get so much more done per GHz than the older P4s that even the slowest Core 2 Duo beats a high speed P4.

If the game specs a dual core processor as the minimum, then you had best have that speed or higher for good software performance.

None, they don't make dual cores that slow.