I want the ability to change lenses :\
If you want the ability to change lenses, then save up more money. MILC is nice but so far it seems really proprietary. I'd say save up your money until you can afford a DSLR with a kit lens and start there. Otherwise, you can get that MILC I linked too up there, it comes with a lens and fits your budget (at least while it's discounted, I saw the body without a lens was almost $100 more), but I don't know how good it is...looking at the specs it does have a few advantages over the FujiFilm, so I'll at least compare those.
Exposure Control: The FujiFilm trumps the Panasonic in ISO sensitivity (160-6400 for Panasonic, 100-12800 for Fujifilm), however the Panasonic does have a better shutterspeed range (60 - 1/4000 sec vs. 30 - 1/4000 seconds). The shutterspeed thing isn't that bad considering my DSLR has a 30 second limit (which works for most things), and I'm unsure if the FujiFilm has a "shutter" mode where you hold the shutter release down for as long as you want. I've confirmed the Panasonic does have this option, but for only up to about 2 minutes. A good "bulb" mode would be as long as you want it to be for, so that's not really a plus.
The EV compensation range is MUCH higher on the Panasonic (-5 to +5 vs -2 to +2 in 1/3 increments), but again, my DSLR has a smaller range and I normally keep it on a set setting. Don't have to change it too often. Still, nice thing to have.
Lens: Before I start with this analysis, I'm only basing the specs of the kit lens for the Panasonic. Of course you can get different lenses, but you're working with a budget and I want to fully compare what you're getting in each package.
The Panasonic has a range of 14-42mm (which should be comparable to 28-84mm on a standard 4/3 lens mount if I'm reading correctly, it has a micro 4/3 mount). This is not too bad for an included lens, most DSLR kit lenses are 18-55mm. Still, in terms of actual usability out of the box, the FujiFilm is going to trump it. The EFL of the FujiFilm is 4.2-126 mm (24-720 mm for a 35mm equivalent), due to it's huge 30x optical zoom. Since it's optical, there wouldn't be any distortion like there is with digital zoom, so that's important to have out of the box. You can buy more lenses for the Panasonic, but that's still going to be expensive and out of reach right away. Here's a list of available lenses for that model specifically to give yourself an idea of specs and cost:
Digital Interchangeable Lenses and Conversion Lenses | PRODUCTS | LUMIX | Digital Camera | Panasonic Global
The aperture is what caught my eye the most. While the FujiFilm has a wider aperture setting (f/2.8 vs f/3.5 max), the low end is where it gets crushed (f/11 vs f/22). For me personally, that may not be a make or break but it's important when you're dealing with longer exposures with certain light sources (say, car headlights). To be fair, f/11 is still decently small for the aperture, but when I shoot those types of shots, I prefer f/16-18 myself.
File Handling: This is where we enter into my make-or-break territory, file handling. I prefer shooting in RAW with my DSLR because it's completely uncompressed and makes it much easier to edit without distortions. The Panasonic does support RAW (I would hope it would considering not many photographers using a DSLR would buy it at an MSRP of $399 without RAW), the FujiFilm does not, only JPEG. Not sure if that's a big deal to you or not.
Bottom Line: The Panasonic is the better camera overall due to it having a larger CMOS, and image quality from what I've shown is close to entry level DSLRs (again, expected to be better than the FujiFilm since it's normally $400). If you must get a MILC then that would be your best option. But make sure you take into account the downside of having a smaller body with interchangeable lenses: with larger lenses it will be awkward to hold.
Personally I would take the Panasonic over the FujiFilm if I didn't already have a DSLR, but if I wanted a supplemental camera for quick shots or fast jobs that don't require the DSLR, I'd get the FujiFilm. I still highly recommend saving money to buy an entry level DSLR instead over either of these cameras however.
