While both the cameras you have there are decent quality, I would refrain from using those only because of the low optical zoom. There are similarly priced (and sometimes cheaper) cameras that have really high optical zooms and respectable quality shots. They're kinda like DSLRs without interchangeable lenses in a way.
I've narrowed it down to three picks within your price range:
Canon PowerShot SX40 HS
Pros: CMOS sensor, supports 4:3, 16:9, and 1:1 format photos, improved image stabilization (3-way), 35x optical zoom, flip-out screen for recording video, lowest aperture/widest range of three (f/2.7 - f/5.8)
Cons: Only 12.1MP (lowest of the three), need to dial down to 9mp to take 16:9 shots, LCD .3" smaller than other two (eh), no HDMI out (other two have this).
Sony Cyber-shot DSC-HX200V
Pros: CMOS sensor, 18.2MP (highest of 3), supports multiple memory card formats, built in 105mb space, highest ISO range (100-12800 vs 100-3200), fastest possible shutterspeed of three.
Cons: Most expensive of three (still within price range), lowest optical zoom of three (30x, still good), have to dial down to 13MP to get 16:9 shots.
Nikon Coolpix P510
Pros: CMOS sensor, Cheapest of three (£248 on bhphoto.com, not sure elsewhere), highest optical zoom of three (42x), 90mb built in memory, lightest of three (though differences in weight are minimal), has a macro setting, not highest MP but is close @ 16.1MP
Cons: Low aperture range (f/3.3 - f/5.9), caps at 64gb for SDXC (may not matter).
To give you some perspective compared to the two you were looking at...the Fujifilm does have a few superior specs, including the CMOS sensor, the ability to shoot in manual with RAW formats, 1080p video recording (think the others I mention only do 720p), faster shutterspeed options and higher ISO sensitivity (same as the Sony I mentioned earlier)...but it's not worth the cost at all, especially considering the 4x optical zoom would be very limiting for any pictures you take. When you start going into digital zoom, the quality degrades immensely no matter how good the sensor or how many MP it has (though it is refreshing to see a lower MP camera with a better sensor)...it's just simply not worth the money. You could buy an entry level DSLR and a lens for that cost.
The Canon is cheaper than any of the ones I linked to, but it shows. The CMOS sensor isn't as good, MP is low, and the optical zoom is also way too low to take advantage of the RAW processing you can do. Decent ISO range, but better to spend a little extra on one of the ones I linked to, you'll get a better bang for your buck. Or pound. Whatever you want to call it.
Downside of the ones I listed are being larger than either of the ones you were looking at, but they are all still very lightweight.
