Is PCGS Actually Better Than NGC?

While I am not a member of either, I believe the preference for PCGS slabs is consumer-driven. I don't think it reflects on NGC's integrity as a grading service.

There is one thing to remember. Whether it be PCGS, NGC, ANACS or any other, there is a human factor involved. Personally, I'm happy about that. However, if you are seeking pure consistency, then the criteria for specific grades needs to be clarified to the highest degree possible. Then, an analysis program can be used to grade without bias.

I think most of us agree that that is not what would be best for the hobby.

I compare it to baseball. I prefer the times when the umpire is correct without dispute and/or replay. Making their rulings susceptible to review and overturning has diminished the umpire's role almost completely. Sorry, a tangent but applicable.

I would add to the first statement.
Slabs are also good for flagging altered coins (cleaned, enhanced, etc.)
The second part is recommended if you can do it yourself.

"Does NGC overgrade coins in comparison, or miss more problem coins? Or is PCGS more reputed by collectors simply because they're more popular?"

My answer to the first question is no and to the second question is yes. I have found NGC to be a very reliable and consistent grading service. When I go to a show, I completely look past the slab and focus on the coin. The TPG is not really a consideration (assuming it's one of the big 3 or 4 TPGs and not a knock off company). With that said, if I wanted a key date coin like a '16D Merc or a '16 SLQ then I prefer it to be in a PCGS or NGC slab because that's what the market commands.

My collection consists of circulated Type coins from the 18th to 20th centuries. I look for original, problem free coins that have nice eye appeal. My collection consists of 22 NGC; 22 ANACS; 19 PCGS; 5 ICG and 2 SEGS and a whole bunch of unslabbed coins. Again, I look at the coin and found decent value with ANACS graded coins even though some may be overgraded by a level or two but I take that into consideration when I purchase it.

My last purchase was a PCGS Seated Liberty dime that was completely missed and undergraded by the company. It was a dime with a polished reverse die Variety (as defined by Fortin) that they took as wear even though the coin was flawless. I got a good value on it though because of their mess-up.

Lately, I have more confidence that an NGC coin will be more solid for grade. Of course I buy the coin and not the slad, but just my first impressions from what I've seen lately.

They do make a lot of errors while grading, and this happens for a reason.

Try spending a good 4-5 minutes examining a slabbed coin. Done? You've just spent 10 times as long looking at it as the grader did.

They have to meet an hourly requirement I think, and they have to grade the coins VERY fast in order to do so.

In my opinion neither PCGS or NGC are perfect. At first I directly submitted to NGC, but they've been rubbing me the wrong way lately. I use PCGS via my friends account, which I have access to. PCGS normally their coins are easier to sell, but NGC isn't far off. It all depends on your preference.