I have not seen any benchmarks, this is only my best guess.
Since the SATA controller has at least double the throughput of an IDE controller, I would say it could "potentially" be faster. But it is irrelevant because the drive will never be able to live up the capabilities/potential of either controller, IDE or SATA.
Take for instance, I think the best IDE controller card you can buy is a ATA133. If the drive is a 133 as well, then there you have it. 133mb/s potential throughput, and that is only advertised rate, you will more likely see somewhere around 30mb/s of sustained throughput, and maybe 60-70mb/s burst with most common drives on a good, fast ATA133 controller. But you must also take into consideration how fast the drive is! Most IDE drives are probably ATA100, and maybe if it is very old at all, it could even be a ATA66 drive. I would hesitate to call a $15 controller card a good card though. But it will likely still run the drive about as fast as it is ever going to run. I would hate to think in this day of SATA devices my PC had parts in old enough that I needed a 4 port IDE card. (added to the already 2 onboard ports) UUUGHHHHhhhhh. Talk about bottlenecks. But, it's up to you.
SATA 1 supports 150mb/s, and you can actually get around 110mb/s burst, and around 80 mb/s sustained throughput with a decent drive, SATA 2 supports 300mb/s, and you can get indeed well over 150mb/s burst speed, and well over 100mb/s of sustained throughput with a good drive.