I'm trying to figure out the best format to serve my tiles. I'm creating an ESRI tile cache. It will be consumed internally through ArcMap from our server, not online. There are a lot of different options. From what I've read, PNG tiles are much larger than JPEG, but have better quality. Does that larger size produce a noticeable different when serving the PNG vs JPEG tiles, or will there be no difference? I'm looking for good quality and performance.
Luckily you do not need to trust in what you read from the web but you can make a test with your own data. It is not as simple as "PNG tiles are much larger than JPEG, but have better quality". That is mostly true with aerial and satellite images which can be compressed effectively with lossy jpeg method. PNG is lossless and quality is thus perfect but the difference in quality between PNG and JPEG may be invisible with bare eyes.
However, if image contains large areas of uniform colors as in topographic maps then PNG may compress more than JPEG. As a simple test I compressed a green box into PNG and JPEG (quality=80%) and file sizes were 8 kB and 30 kB, respectively.
Make a test with your own data and base your selection of cache format on that. Another thing to consider is that JPEG compression is doing bad for sharp edges like texts in printed maps.
The speed of serving tiles depends only on the file size of the tiles. If the difference is notable or not depends on the band width and total load on your server. If you will read the tiles locally I bet you will not feel any difference at all and if you feel it comes from the client which handles either PNGs of JPEGs better.