Looks like that you are doing viral induced gene silencing (VIGS) experiment. Seems that the two binary vectors (pTRV1 and pTRV2) contain two major different genes, pTRV1 contains RdRP (RNA depended RNA polymerase) and pTRV2 contains a 'target gene' (if you insert a gene in it) you are aiming to silence in the plants (see attached maps). These genes might cause the different growth rates of Agrobacterium hosting them.
Except mentioned two genes in my previous answer, the vectors also contain 'MP' (Movement Protein) and 'CP' (Coat Protein) of virus particle in pTRV-1 and pTRV-2 respectively (see previous attachment). Both of the constructs are also driven by 2x35S promoter, which is active in Agrobacterium. Therefore, these genes can be expressed in Agrobacterium and affact the growth rate of Agrobacterium cells.
If your are using TRV-based binary vectors (pTRV-1 and pTRV-2) for your virus-induced gene silencing (VIGS) research, I found the attached paper is very useful, in terms of technique. They even included information of what 'size' of the targeted endogeous gene should be used (see below). I think that is an important piece of info to know. And, criticle for the experiment to work.
"Gene fragment chosen for silencing: Fragments of 300-1500 bp have been used successfully to induce VIGS. Silencing efficiency is reduced below 300 bp, whereas with longer fragments there is a strong possibility of the insert being lost from the recombinant virus."