Oversized A/C systems come up short, dry, and sticky
Most people treat air conditioning in the same fashion as they handle heating: namely, as a simple mover of BTUs. However, that isn't quite true, otherwise we wouldn't have condensate coming out of our indoor units. The truth of the matter is that air conditioners both cool air and dehumidify it, at the same time, and have two different capacity measurements as a result. However, manufacturers lumped both functions into a single BTU sizing number for a given set of conditions. The proper sizing procedures using Manuals J and S take this into account (note that even an aggressive Manual J calculation with no padding at all will still yield a somewhat oversized system, just not a grossly oversized one); however, "rule of thumb" sizing does not.
Worse yet, the ratio of latent (moisture removal) to sensible (direct temperature dropping) capacity an air conditioner supplies is not constant. Instead, it depends on the speed of the indoor blower and the ability of the air conditioner to run long enough to get condensing conditions on the indoor coil (i.e. the indoor coil needs to be colder than the dewpoint of the air). With a grossly oversized system, the indoor blower speed will be high, leading to very little "residence time" for a given parcel of air to hang out near the coil and give up humidity. Worse yet, the air conditioner will only need to run briefly to reach the temperature setpoint, meaning that the indoor coil never gets below the dewpoint of the air and you get none of that wonderful condensate coming out of the drain pan. Instead, you get a house that is cold, clammy, and downright icky, as all that humidity is now sitting in air that's much colder than the outside air.
Avoiding this is simple: do not go above proper Manual J, Eighth Edition numbers for a house, ever. In fact, it is indeed more acceptable to slightly undersize a system and not have perfect temperature control on one or two days of the year than to grossly oversize it and find yourself wondering why the air conditioning is making your life miserable.
There is a caveat to all this, though
There is one caveat to what I just said, and that's that Manual J/S sizing assumes that your house has properly designed ductwork, as per Manual D. Improper ductwork can cut your HVAC system's net effective capacity by 25% or more; sadly, this is not an uncommon situation in the American South, where "lob a bunch of flex into the scorching hot vented attic and call it a day" is all too often the way it's done. As a result, many systems wind up oversized to compensate for the sloppy, crappy, money-wasting, energy-hogging nightmare known as a 'ductopus' that invaded someone's attic.
As a result, you'll want to have your HVAC installer banish any metallic many-tentacled monstrosities currently present from your attic when they put the new system in. If you can't bear to have the ducts dropped into conditioned space, then you'll want to go to an unvented/conditioned attic instead, or at a minimum use a steaming heap of spray foam to encapsulate them thoroughly, although the latter's only practical if the air handler's in a closet, not sleeping in the attic next to the ductopus that's trying to strangle it.