Iphone 5 vs Note 2 vs Blackberry Z10?

Which phone has the overall best performance in all aspects?

This really depends on who you ask. The processor on these have absolutely no bearing on the actual speed of the OS or apps. Why? Because all OS are built differently, they react differently. Most people complain that the iPhone is sluggish compared to the Note 2 (and Galaxy S3) and Blackberry Z10.

For the number of apps they offer, you're better off with the iPhone or Samsung.

If you want security, your best bet is the Blackberry Z10.

If you want what's being called the best touchscreen typing experience on the market right now, that's the Blackberry Z10.

NOTE 2 All THE WAY.
Advantages of the Note 2:
Quad-band GSM and quad-band 3G with 21 Mbps HSDPA and 5.76 Mbps HSUPA support
Optional LTE connectivity
5.5" 16M-color Super AMOLED capacitive touchscreen of HD (720 x 1280 pixel) resolution; Corning Gorilla Glass 2
Android OS v4.1 with TouchWiz launcher
1.6 GHz quad-core Cortex-A9 CPU, Mali-400MP GPU, 2GB of RAM, Exynos 4412 Quad chipset
S Pen active stylus with deep system integration
8 MP wide-angle lens autofocus camera with LED flash, face, smile and blink detection
1080p HD video recording at 30fps
16/32/64GB internal storage, microSD slot
Dual-band Wi-Fi 802.11 a/b/g/n support
GPS with A-GPS connectivity; GLONASS support, Digital compass
NFC support
Stereo Bluetooth v4.0
FM radio with RDS
microUSB port with USB host and TV-out (1080p) support, MHL, charging
Accelerometer, gyroscope and proximity sensor
Standard 3.5 mm audio jack
Great audio quality
Very slim at only 9.4mm
1.9MP secondary video-call camera
Document editor and file manager comes preinstalled
Extremely rich video and audio codec support
Huge 3100 mAh battery

You can also read this:
http://au.ibtimes.com/articles/388522/20120927/samsung-galaxy-note-2-better-iphone-5.htm