There are times when a table explains things so much better than just text.

From BizTalk Server 64-Bit Support:

Which versions of 64-bit Windows are supported?
All versions of BizTalk Server 2006 support 32-bit execution on Windows Server 2003 x64 (including R2) and Windows XP Professional x64 by using WOW64. Additionally, BizTalk Server 2006 Enterprise, Developer, Branch, and Evaluation Editions support native 64-bit execution on Windows Server 2003 x64 (including R2) and Windows XP Professional x64 by installing both 32-bit and 64-bit executables and providing configuration options to use either 32-bit or 64-bit modes. 

 which means:

Edition

32-bit execution by using WOW64

Native 64-bit execution

on Windows Server 2003 x64 (including R2) and Windows XP Professional x64

Branch

Yes

Yes

Developer

Yes

Yes

Enterprise

Yes

Yes

Evaluation

Yes

Yes

Standard

Yes

No

Here's the justification (that I've borrowed from an official response on one of Microsoft's forums):

"We consider 64-bit support an Enterprise Edition level feature that a customer would only select if they require faster messaging/orchestration processing or the larger addressable virtual memory of 64-bit mode for large BizTalk message mapping or other memory intensive operations. Because the Standard Edition is designed for small-to-medium environments, it is licensed to only run on a single BizTalk server with a maximum of two CPUs, maximum of five "BizTalk Applications", and a single message box. 64-bit support for the Standard Edition seemed counter-intuitive from a technical and licensing perspective. If the deployment scenario requires 64-bit hardware then it certainly requires BizTalk Enterprise as well. Standard edition is for single box only installations. Enterprise is also required for multi-box installs and for clustering."