BREAKING! Optical media slower than game cards.
I guess it's nice to know how much the difference is though, but it's not exactly very useful. It's not that bad in either case here.
For the 6x Bluray reader on the PS4, Ps4pro and XB1 the maximum read speed is about 27MB/sec. The Bluray players on both consoles are primarily used to load games from the media onto the storage device be it 5400rpm HDD (approx 80MB/sec to 110MB/sec reads - depends on brand), 7200rpm HDD (approx 23% faster than 5400 rpm), Hybrid HDD (approx 80MB/sec to 500MB/sec - for SSD part) and SSD (approx 500MB/sec).
The read speeds given above depend on the brand with write speed 20% to 30% slower.
Unless you have a class 10 high-performance SD card or cartridge you may have a read performance of approx 250MB/sec but you are going to pay for that performance. A cheap SD card may only have performance figures of 25MB/src read with a reasonable class 10 SD card having an average performance of 50MB/sec reads.
Without knowing the full engineering specifications of the Switch I can't comment on its internal "bus" which could be SATA 2 (300MB/sec) or SATA3 (600MB/sec - PS4pro) but I very much doubt it could be SATA Express (up to 16Gb/sec) or PCIe (up to 32Gb/sec) which is what my desktop PC has and there are better performing motherboards out there as well.
Now that I have probably confused you (sorry about that) lets put things is a more simple perspective.
When you start a game or even an application you will normally get what can be described as advertising which in the case of say Breath of the Wild will be the Nintendo logo as well as some other information such as graphics engine(s) and there are deliberate delays so that the user can see them. On the PS4 you get exactly the same type of advertising (the XBox will be the same) and depending on the game the advertising part may be anything from a minute to a few seconds.
As an example: I have my Linux operating system for my desktop on an SSD. I click on say Google Chrome and I can barely count to one second before it displays on the screen, yet there are applications that can take up to 15 seconds (most are usually less than five seconds) before being displayed because of so-called advertising. On my PS4 its web browser takes about three to five seconds to start.