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The 01 will have a bit more horsepower and torque due to the LS6 intake that came standard. I it's 5 hp more and 10 foot pounds for auto and 15 for standard.
I think the driveshaft/torque tube was also upgraded
I had a 99 with almost 100k miles with no major issue, but the ABS crapping out is always a possibility. I sold it in May and picked up a 2003 with 32k miles. The moral of the story is that there are lower mileage 02-03 Vettes out there to be had.
welcome to the forum! Condition and how the cars were cared for is the most important. However, with no other info, I would get the '01. It's slightly faster. It has newer components that are cheaper and easier to replace (some parts on the '99 are no longer made). These cars were designed to be driven. If they sit, they tend to develop certain issues. The '01 was driven regularly, but was still driven less than 3k miles a year. That is the sweet spot for mileage on these cars. As an added bonus, the '01 is actually cheaper. The most important thing though is to get a pre-purchase inspection done before you buy. It is worth every penny. Good luck! Let us know what you decide.
Even more important, can you work on it yourself or need a Ace mechanic???.
As stated already ,, the 2002, 2003 are preferred year C5 choice. Don't rush into a decision, especially bases on miles, consider all aspects of the car. You'll get tons of help here, Use everyone's wisdom wisely.....
Enjoy the search and be patient. The right one will find you,,,,