This is actually a great question and I'm grateful for all the responses thus far. I'll try to be as unfiltered as possible, taking off my green sock for a moment
File size - GSAP does a LOT for you, solving browser inconsistencies, delivering a ton of features, blah, blah - that takes some kb. Sure, there's a CDN and GSAP's ubiquity makes the file size a non-issue in many cases, but the reality is that TweenMax is larger than most other animation libraries and if you're bundling it in your own JS file (like a Webpack bundle), it can be a tad heavy if you're only using it for a few little things.
License/cost - even though the vast majority of use cases qualify under the standard "no charge" license, some might require the special commercial license that comes with "Business Green" Club GreenSock memberships. It's not "open source" in every sense (yes, you can view the source on Github but that's not the same thing). And some of the plugins are only available to club members. I argue that the license is actually a BENEFIT, not a drawback, but some people may feel differently and that's okay.
Main thread - this isn't specific to GSAP, of course, but some would argue that CSS animations and WAAPI can get better performance than any JS library when it comes to animating transforms (scale, rotation, translateX/Y) because in some cases (when NOTHING else is animating except transforms or opacity, and the main thread is super busy, and there aren't too many transform tasks), transforms can be spun off to a different CPU thread. Sometimes that's indeed useful and can result in less jank. That being said, I've seen several cases when GSAP is actually faster than WAAPI and CSS, so it's not fair to make a blanket statement that JS libraries are always slower. https://greensock.com/js/speed.html
I think that about sums up the "negatives" that I've heard in the past. Of course I want to chime in with a ton of counter-arguments that dwarf the negatives, but that's not what you asked for
As for Snap.svg, that's more of a library for creating and interacting with SVG elements, not so much animating them. Even the author of Snap.svg said that GSAP is probably the best thing for animating Snap.svg objects. So I wouldn't say that Snap.svg and GSAP are competitors at all - they're complimentary. GSAP is focused on animation - you can't create SVGs with it. Likewise, the author of Snap.svg said it wasn't designed to do complex animations.
Does that help?