. IF your GOI is a gene from an eucariotic organism (eg. human) and it contain several rare codons from E.coli, Rosetta could be a possible soluton while if there is any issue of rare codon you can skip to use it, since for the maintanance of the 2nd plamid (pRARE) those codify for the rare codons, you need to use a 2nd antibiotic which slow down the bacterial growth and do not allow to obtain the same growth rate and final biomassess than are obtained in standard BL21. On the other hand for example in case your gene codify for a protein with contain some Cysteines involved in S-S bond, the origami strain could be an other solutiion.
i forgot to mention the pGEX is based on Tac promoted wich differently to the T7 promoter do not require the T7 polimerase but it work with the standard E.coli polimerase so you can use also non DE3 strains (eg standard BL21, Origami, Rosetta, W3110).
This promoter is not strictly regulated as the T7 so basal expression prior IPTG induction is possible.
pGEX-4t1 is an AmpR plasmid containing ptac promoter. This is an IPTG inducible promoter. You don't actually need the DE3 lysogene in your recipient strain (DE3 encodes for the T7 RNA pol under the control of an IPTG inducible promoter) as IPTG is a direct inducer of ptac promoter. Therefore using rosetta DE3 is a bit of a waste as the T7 RNA pol will be useless. Use normal Rosetta instead if you really need pRARE and IPTG induction. Don't forget to select for both plasmid in Amp+Cm containing medium.