[R] SEM model testing with identical goodness of fits

[hyena]

HI,

   I am testing several models about three latent constructs that 
measure risk attitudes.
Two models with different structure obtained identical of fit measures 
from chisqure to BIC.
Model1 assumes three factors are correlated with  each other and model 
two assumes a higher order factor exist and three factors related to 
this higher factor instead of to each other.

Model1:
model.one <- specify.model()
	tr<->tp,e.trtp,NA
	tp<->weber,e.tpweber,NA
	weber<->tr,e.webertr,NA
	weber<->weber, e.weber,NA
	tp<->tp,e.tp,NA
	tr <->tr,e.trv,NA
	....

Model two
model.two <- specify.model()
	rsk->tp,e.rsktp,NA
	rsk->tr,e.rsktr,NA
	rsk->weber,e.rskweber,NA
	rsk<->rsk, NA,1
	weber<->weber, e.weber,NA
	tp<->tp,e.tp,NA
	tr <->tr,e.trv,NA
	 ....

the summary of both sem model gives identical fit indices, using same 
data set.

is there some thing wrong with this mode specification?

Thanks