I store my tilemapgrid in a 32-bit .tga, which automatically rle-compresses to 3k.
That may be true, but it isn't the complete story, or I could just draw my entire level as a single bitmap and then say it only occupies 1 byte because I have a 1x1 tilemap referencing that bitmap!
Anyway, file size considerations aren't really that relevant. In a tilemap you pay for level size and level complexity, but increases in complexity are hard to quantify because they take effect partly through requiring a greater variety of tiles and partly through crushing whatever compression you're getting on your map.
In a vector map you pay only for complexity, to an extent size comes "for free". But compression isn't so obvious, in particular for repeated sections of level or if you want to expand your level. If you use a sectoring system, you can get a lot of position information implicitly, the same way that the world positions of tiles are implicit from a tilemap. In that case you could probably use fewer bits to store coordinates.
Another form of vector map would just involve a whole load of reusable segments that are positioned, arbitrarily stretched/rotated and combined to form the map. Then you can build some very complicated maps using very little storage. It also depends what you want to do with your map. Suppose you just wanted a series of loops, jumps, etc, for a game like the SNES game Uniracers. Then you could construct some curves and some loops, and just store a linear sequence of the order they come in. Position and orientation are implicit from the other pieces encountered to date. That approach would yield a non-tilemap approach that was absolutely tiny compared to the tilemap equivalent.
This is all a bit of a false debate though. Nobody picks their map format based on memory footprint when both types are so tiny compared to available resources. And the fact is that for some purposes a tilemap is smaller, for some it is a vector map.
In case anybody does want to turn this into some sort of holy war, I cite now the example of Acornsoft's Citadel for the Electron*/BBC Micro that uses a vector map on an 8bit micro with only around 20 kB storage total once the framebuffer and OS buffers are removed, and manages an interesting and large level.