This is a really good question as there are few more out there and some that are no longer with us in which they have graded a substantial amount, so where does your trust start and end ?
If bidding sight unseen, aka from eBay or an online seller where you can’t physically hold it, then PMG and PCGS are solid choices that usually don’t lie on grades. If the note happens to be in a bottom feeder holder, then unless the price is so low that you can get it grade by a reputable company, get the grade you want, and then sell it for more than you bought it for less fees Then again I’m just a guy who doesn’t care about resale value of his collection itemsz
PMG since the git go but I'll trust PCGS now that it's under CU. There's some notes you can buy raw because it's against the law to sell counterfeit US currency. Now I do not believe the law applies to Obsolete or Confederate currency. So, I buy on the safe side. PMG graded. Just my opinion; nothing more.
I tend to buy colonials in PMG or PCGS, (mostly PMG). I buy the note, so do not care what the grade is from the TPG, but since the types of notes I buy tend to be pricey, and I do not trust my counterfeit detection skills on notes as well as coins, I buy them certified to make sure genuine.
If I'm working on a graded set, I like them all to be in the same holder. Otherwise, I tend to stick to PCGS and NGC.
As you can see by the above examples "Trust" is a huge part of grading after many years as a collector, I have only experienced a handful of point differentials and only 1 point either way but a 63 to a 66 ? , this note has no business being in a 63 holder ! when I got regraded by PMG I new that I was right
Since the cost of the bill in the holder, is going to be higher or lower depending on the grade buying the note raw might be a consideration for you ?