There are four major issues with pH selection:
- column lifetime
- method robustness with respect to minor pH variations
- retention
- selectivity.
Taking them in reverse order:
1 selectivity is always a gamble. The only way to find out is to do the experiment.
2. Retention is reversed-phase will depend on the degree of ionization, with the neutral form of a molecule being more strongly retained than the ionized form. If the rest of the molecule is sufficiently hydrophobic, you can get reasonable retention even with an ionized functional group.
3. Robustness with respect to pH is generally the worst at or near the pKa (that's where retention changes most rapidly as a function of pH) and generally the best 2 or more units away from the pKa. The exact meaning of "worst" and "best" depend on the details of the specific molecule and system. Note that "lack of robustness" is essentially synonymous with "extremely fine control of selectivity"

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4. Column lifetime is generally best between pH 3 and pH 7, and falls off outside that range, unless you are using columns designed (and promoted!) for high or low pH operation.
I'm assuming your compound has two acidic groups. In that case, running near pH 6 will have the low-pKa group ionized and the high-pKa group neutral. If the rest of the molecule is sufficiently hydrophobic to give reasonable retention, you should have a reasonably robust method. Running at pH 2.1 or thereabouts (0.1% TFA) will have the low-pKa group slightly ionized (if you are 1 pH unit below the pKa, you will have approximately 10% ionization). That should give you greater retention, and may give you some control over selectivity, but may also result in less robustness with respect to pH.
It's hard to tell what is the "better" choice without trying both!