VIT Vellore is better. It is among the top engineering colleges in the region. It has a wonderful campus, good infrastructure, and a decent placement record. The departmental laboratories are well-equipped with rare equipment such as AFM, STEM, XRD, etc. VIT has a digital library with a huge collection.
The highest CTC offered during VIT Vellore placements 2022 was INR 75 LPA. Paypal, DE Shaw, and Dyte were some of the major recruiters to take part in the placement drive. The placements are especially good for branches such as CS, ECE, IT, Mechanical, etc.
By Anna University, I will mean the three constituent campuses; College of Engineering Guindy (CEG), Madras Institute of Technology (MIT), and Alagappa College of Technology (ACT), and not the affiliated colleges spread all over Tamil Nadu.
Anna University is a government university while VIT is a private university. Obviously, there is a huge gap in terms of fees and the overall infrastructure. VIT offers a very posh campus but has a considerably higher fee than Anna University.
However, which one is good for you is up to you only and I cannot tell what do you want in your life.