Unless you have the need for the rare codons supplied in Rosetta strains i would recommend to stick with regular BL21. Rosetta is essentially BL21 (and also available in K12 variations) with the added plasmid pRARE coding for several rare codon tRNAs. This is an obvious advantage if your gene of interest have many of these rare codons. However, it comes at the cost of having an extra plasmid in the strain. This puts several limits to your production strategy 8which may or may not be a problem for you). For instance:
*The plasmid pRare in Rosetta strains is based on the p15A ori, meaning that you are limited to using colE1-based plasmids (for instance pBR,pUC, pET).
*pRare also carries it's own antibody selection marker (chloramphenicol, tetracylcine or kanamycin depending on which version of Rosetta you have).
*The expression of the extra plasmid probably puts a bit more metabolic burden on the cell compared to BL21. I have no personal experience of this however, so I am not sure how big of an impact it has on for instance cell growth rate.
Rosetta\Rosetta2 are BL21 so there is no different between them for bacterial expression. for eukaryotic it butter to use Rosetta because they have rare codon.
If your protein has rare codons, then better use Rosetta otherwise stick to BL21 (DE3). In my experience there no difference in transformation success.