How do cis-regulatory elements and trans-regulatory elements behave differently?
I was thinking cis would be favored because the gene is close by


Your intuition is correct.  Cis-regulatory elements like enhancers are more efficient at enhancing transcription of genes in cis than genes in trans, but trans interactions of cis-regulatory elements do occur.  Take a look at figure 2B of this paper and the accompanying text:


  ... quantitative RT-PCR showed that relative levels of GFP transcripts from constructs inserted at 37B were similar to those from transgenes at 53F, with 1.7% [95% C.I., 1.6–1.8%] of total GFP transcript in eye discs where GMR acts in trans relative to those where activation is in cis ...


The interaction of alleles between homologous chromosomes is called transvection, and this can be realized as binding of the enhancer associated with one allele to the promoter of the other allele.  Figure 9 of this paper is a good explanatory graphic.