The closest thing to Draw's Add Perspective feature in Illustrator is an awkward modifier key combination while using the Free Transform tool.
Select the object(s) you want to distort.
Get the Free Transform tool. A bounding box appears around the selection.
Mousedown on one of the corner handles of the bounding box. Press and hold the Ctrl and Alt keys. Drag.
You'll get a logarithmically "foreshortened" distortion much like that with Draw's Add Perspective. However, it is not nearly as useful. It does not provide the perspective grid that Draw's feature does. You can work around that by drawing a grid as part of your distorted artwork; but that's cumbersome. Moreover, though, you'll find that as soon as you mouseup after doing the "perspective" distortion, the bounding box returns to a rectangle. So subsequent adjustments of the perspective proportion are very awkward and haphazard.
Do not confuse Illustrator's 3D Effect with Draw's Add Perspective or Interactive Perspective Tool. Those are 2D transformations for doing straightforward 2D perspective (oblique projection, vanishing point perspective, isometric drawing), quickly and interactively generating a clean set of vector paths.
AI's 3D Effect is an actual 3D modeller. It uses the paths you apply it to as the sections of a 3D model; then renders that model as vector artwork. The result is more realistic in both shape and shading, but consists of many more objects including clipping paths. Even turning off the rendering by using the Wireframe shading option results in more paths than you want for linework perspective drawing.
3D Effect is not on-object interactive. You revisit a modal dialog to edit it.
Using 3D Effect, Effect>3D>Rotate (not Extrude & Bevel) would be more akin to the kind of thing you would use Draw's Add Perspective for. 3D Rotate projects your artwork onto a plane in a 3D model, which you can then orient in the modal dialog. However, it outlines strokes in your artwork, so it's not really as useful for 2D perspective construction of a drawing in which you will be doing alot of edting and building upon.
3D Extrude & Bevel is more comparable to Draw's Extrude feature (although Draw's Extrude is also actually 2D). For the kinds of things you would use Draw's Extrude for (creating finished individual "3D" objects) the results of 3D Effect would be vastly better in most cases.
So AI's 3D Effect is actual 3D, intended more for creating finished simple 3D objects. You can do neat things with it, and Draw doesn't have anything really like it.
Draw's Add Perspective and Interactive Perspective Tool are 2D features, intended more to facilitate quickly and interactively "sketching out" and setting up construction for 2D perspective drawings. You can do neat things with them, and Illustrator doesn't have anything really like them. (Excepting the perspective trick with the FreeTransform tool, described above, which is significantly inferior.)
JET
