[R] which to trust...princomp() or prcomp() or neither?

[Blair Smith]

According to R help: 
princomp() uses eigenvalues of covariance data.
prcomp() uses the SVD method.

yet when I run the (eg., USArrests) data example and compare with my own 
"hand-written" versions of PCA I get what looks like the opposite.
Example:
comparing the variances I see:

Using prcomp(USArrests)
-------------------------------------
Standard deviations:
[1] 83.732400 14.212402  6.489426  2.482790

Using princomp(USArrests)
--------------------------------------
   Comp.1    Comp.2    Comp.3    Comp.4
82.890847 14.069560  6.424204  2.457837

Using my custom pca_svd() --- (my PCA method using native R svd() function):
-----------------------------------------------
$stdev
[1] 82.890847 14.069560  6.424204  2.457837

Using my custom pca_cov() ---  (my PCA method using native R cov() and eigen() functions):
-----------------------------------------------
$sdev
[1] 83.732400 14.212402  6.489426  2.482790

You see the problem: my SVD method yields results numerically similar to 
the princomp() method which supposedly uses the eigenvector calculation.
Whereas my eigenvector calculation method yields results numerically 
similar to the prcomp() method which supposedly is a SVD calculation!

Also, it surprised me that the two methods would differ so markedly (only 2 significant 
figure agreement at best).  Ultimately the question is which method to trust as most 
accurate?  

When I get time I'll just put in some data with KNOWN PC stdevs to see, but I'm 
still curious to see if any of you reading this help list could explain in advance?

If any R gurus or the writers of either of the aforementioned routines can
enlighten me I'd be most grateful.

---
Dr Blair M. Smith
Industrial Research Limited
NZ