I can't say which would be better emphatically since I'm not sure what you would like to do specifically with either machine, but I can give you some insight so that you can make a decision.
3d printer:
Overview:
In your price range you would be looking at an FDM type machine (extruded ABS, PLA etc.). Having used some lower end machines in this price range my advice would be to look for a printer that has the best overall quality vs size of build platform. I spent so many hours tuning and tweaking my last low end printer. Also many of the low end machines boasting large build platforms miss a major point. You cannot make large prints especially out of ABS without a thermal chamber. Its a complicated process, but its mostly due to the contraction of the plastic as it cools. Some folks love tweaking and playing with these printers, but I just wanted to build stuff I could use. 20/20 hindsight proved I would have been better served using Shapeways, which is a great option by the way.
Despite my feelings about experience with some of the low end machines, consumer grade printers have advanced a lot. The Makerbot Replicator Mini looks to be a quality machine in your price range. They apparently addressed many of the typical annoyances (putting it lightly) such as leveling of the build platform. If I were to go with a 3d printer in your price range, that would be my pick.
Advantages to the technology:
With a 3d printer you can make fairly complex parts, that would in many cases be impossible for a 3 axis router to build.
3d printers are for the most part fully automated. You just press print, and come back in a few hours.
Disatvantages to the technology:
Repeatablily- lots of printers in this price range can be irritable. If you print the same thing multiple times you will probably notice some variances.
Its an additive process. So you need to factor in the cost of filament into your budget. Its typically more expensive than raw materials you would cut with a CNC.
Maintenance- to keep a printer running smoothly you need to make sure the extruders are not getting clogged; the build platform is level and clean so on and so forth
limited material selection- Some parts you may want to build will not be well suited for the materials you can print with
Grain boundaries- When you print layer by layer there is a defined grain to the part similar to a piece of wood. If you load an RP parallel with the grain it will be more prone to shearing along the grain.
CNC router:
Overview:
A CNC router is a powerful tool, that is really optimized for 2 1/d work. Meaning you can cut 2d shapes out of a block of material. The 1/2 d being a plunge of a given depth. That being said it is possible to create full 3d cuts, but this requires a range of tooling, and more advanced software, that may or may not be available in your price range. Be aware that many routers at the low end cut corners with build materials. Try to stay away from routers built from materials such as masonite manufactured wood and particle board, since these materials are highly sensitive to moisture, which causes warping. You may be able to treat or coat such materials to better weatherize them, but this could also disrupt the fit of the parts, which is bad too.
One of the biggest differences from 3d printing to routing is that you have to be aware of the cutting tool limitations. In the case of a router, milling of the material constitutes horizontal cuts with a rotating blade of some diameter. You cannot cut a square hole with a drill bit that you would put in a cnc router. So you need to think in terms of what features are reasonable or possible for the machine to make. 3d printers don't really suffer from this issue since they extrude minuscule amounts of material layer by layer. As such the extruder is always above the work piece.
Advantages:
generally have a larger build area (l x w) than 3d printers of the same expense
Vast material selection
More repeatable than FDM 3d printers (in my opinion)
Generally better resolution than comparable 3d printers
Disadvantages:
Tooling- all the drills and routing bits. You have to be careful when you design not to require exotic features that would require equally exotic tooling
Wear- The tooling used has a finite life span. As the tools become dull you need to replace them. Worn tools can break and produce poor results.
Tool changes- routers require different tools for different features when cutting in 3d. You have to babysit these machines to change out tooling.
Noisy
produces lots of debris
Closing:
If I were in your shoes, and wanted to make robot chassis I would consider what kinds or parts were important to me. If you want to make cool/intricate 3d parts I would go 3d printer or shapeways. If my goal was to make larger, and more robust parts, that were primarily 2d in nature, a CNC router would be the way to go.
Hope that helps