After trials with earlier versions, the Pi and Pi2 updated to Kernel 3.19.3 without too much effort..

Source from here:  https://github.com/raspberrypi/linux/tree/rpi-3.19.y

Pi:

Pidora release 2014 (Raspberry Pi Fedora Remix)
Kernel 3.19.3 on an armv6l (ttyAMA0)
........
]# uname -a
Linux rgpi 3.19.3 #1 PREEMPT Fri Mar 27 23:55:44 PDT 2015 armv6l armv6l armv6l GNU/Linux

Pi2:

Fedora release 21 (Twenty One)
Kernel 3.19.3-v7 on an armv7l (ttyAMA0)
.............
]# uname -a
Linux rgpi2 3.19.3-v7 #1 SMP PREEMPT Sat Mar 28 00:50:19 PDT 2015 armv7l armv7l armv7l GNU/Linux

I also discovered the source of the ‘sluggish’ performance of the Pi2 – I had accidentally put an older version of the boot binaries etc. in the /boot directory, which resulted in only 256MB of total memory!

Robert Gadsdon.   March 28, 2015.