Any chance you can post a small clip as an example?
Typically, when Max renders, it’ll interpolate between any frames, whatever frame rate you have in max. So unless you have some whacky curves that force the animation to change every frame, or otherwise have pre-baked animation that’s being rendered at a different frame rate to which it was captured at, you should always get a smooth result. Once it’s out of max, it’s just frames - how that’s then interpreted by After Effects is, likewise, irrelevant to the frame rate in Max.
As such, I have to assume that your problem is in AE. Do you have a copy of another video editor you could test it on? Perhaps Adobe Premiere? Or otherwise use 3ds Max’s “Ram Preview” (Rendering -> Ram Preview -> Open Channel A). In this, you can vary the frame rate all you like, and it might give you some idea as to how it really looks once rendered.