ASMedia is the only controller IC manufacturer that can be trusted for these IME. They also have the best Linux support compared to the other options and support pass-through commands. These are commonly found in USB DAS enclosures, and a very small fraction of single disk SATA enclosures
Innostor controllers max out at SATA 2 and lock up when you issue pass-through commands (e.g. to read SMART data). These also return an incorrect serial number. These are commonly found in ultra cheap desktop hard drive docks, and 40pin IDE/44pin IDE/SATA to USB converters
JMicron controllers (not affiliated with the reputable Micron) should be avoided unless you know what you are doing... UASP is flaky, and there are hacky kernel boot time parameters required to get these working on Raspberry Pi boards. Unfortunately these are the most popular ones on the market due to very low cost