T7 vs pBAD promoter strength
The exact numbers depend on the protein.
In my hands, I would say between the pAraBAD and a pLac-T5 you can expect some fold improvement and pAraBAD and a pT7 promoters you can expect about an order of magnitude… but there are two big caveats.
First, pET and other T7 driven plasmids do not work in K-12 strains (without the pTARA) so BL21 is generally used. BL21 is much better generally than K-12 strains (more primary metabolites cf. omics paper) for a lot of things including protein expression. The chaperone balance is difference, so you will get differences from that too —if you have used the TAKARA plasmid team you will have notice how quirky protein expression optimisation can be.
Second, if your protein has a cofactor you have a major problem. FeS clusters, PLP, heme or even O2 (for maturation of GFP, say) become rate limiting and overexpressing the protein can make it highly toxic and you might be in a bigger pickle than with a lower level promoter. In my thesis, I added pyridoxine to a pBAD expression, because it gave an improvement.

Footnote: If the expression levels are really bad, changing promoter might not be that great as the assumption of linearity might not hold.
If heterologous and not codon optimised, consider using pRARE.
If insoluble, consider using ethanol shock and the TAKARA chaperon plasmid team.
If oxygen sensitive, alas, doing expression and purification anaerobically.