It's likely to be the effects of confounding among the variables. The AOR will be slightly different from the AOR and there's no particular reason it must be smaller. Check that you are fitting the two models on the same sized data sets (i.e. some cases may have been excluded in the larger model because of missing values in other variables, introducing bias in the OR of interest).
I agree with Steve
There can be two reasons for a difference between the AOR and the UOR.
First, if the UOR is conducted on a different dataset then the AOR. The bivariate logistic regression that produces the UOR will only exclude observations pairwise (aka available case analysis) whereas the multivariable model that yields the AOR will exclude observations list wise (aka complete case analysis). If values for the different variables are systematically missing, problems will occur.
The second reason for differences (as Steve and Stephanie mention) is confounding itself. That is, the statistical control of a third variable (or set thereof) will alter the association between our outcome (e.g. disease status) and study effect (e.g. exposure). In fact, Hosmer, Lemeshow and May (2008) give a nice way of empirically defining a confounder as something that changes our coefficients (or ORs, RRs or HRs etc) by some pre-defined amount (e.g. 10%). They do this as part of their '"purposeful selection of covariates" model building strategy in the contexts of hazard ratios from a cox regression, but I believe earlier work by Hosmer and Lemeshow also considers the problem in a logistic regression context. The fact is, the idea is just as valid for Logistic regression.
Certainly changes in AOR from UOR is one way that people talk about whether or not confounding was present and adjusted for (for better or worse).
After seeing too many people not notice that their datasets were different between the two different analyses, due to missing data in the additional covariates added in the model, I can't underscore enough how important it is to make sure that the AOR and UOR are using all of the same observations.
If UOR is different from AOR it is mainly because of the confounders
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