from my findings and the most trouble free way to flash things, especially if your useing fk23 and/or most if not all JB "stock TW (touchwiz) roms, is use agats latest 6.8 kernel+recovery.
I've posted in a thread how to do stuff so you'll have to do a search, but in short you use agats6.8 as a temp recovery and reflash back stock fk23 (kernel only) when done flashing everything else.
Remember that there are roms out there that are JB roms, but there is a difference in JB roms and JB "tw" roms, so you need to use whatever recovery accordingly.
A short explanation would be cm based roms (AOKP/AOSP/CM10) are all JB roms, but.....they are NOT jb "TW" roms, so you would want to use a cwm recovery with those (not agats) as agats is mainly and almost always for stock TW roms. I'm not sure what roms are stock TW roms, except for 3, that is FI22 and FK23 and FL04.
@elpapirin
for the modem you need to flash the modem only zip file from recovery, again I recommend agats6.8. Keep in mind NO rom out will flash your modem, none, EXCEPT for the stock roms, which come bundled with the Kernel+rom+modem, so in short.....ONLY stock roms will flash the modem, other roms will only do the kernel and rom only, so you will always have to find a modem you want to use.
Most all files kernel and modem and recovery can be found at this site
Rwilco12's Android Repository. Remembering the above rules you should be ok. So if you want to go back to the fk23 modem and not touch the rom+root, just grab the fk23 modem zip file from that link and flash it via agats6.8 recovery.
One Clicks = PC only
Zips = Recovery only
Tar = Mobile odin and PC only
(please correct me if this order is not correct)
Mobile odin does not flash modems, so keep that in mind. Mobile odin is also not free, it costs and is in the market if you wish to d/l it. I did and it's been SO much of a life saver for me, but it's preference really.
A short how to again:
"Method 1 - The recovery way"
1: Mobile odin or PC odin agats6.8 recovery
2: reboot
3: for me it went past the Samsung screen and went black, but that's ok don't panic, count 1001, 1002, 1003, up to 1010 then hold power+vol up keys at the same time until you get to agats recovery. The reason I wait 10 seconds is so it can fully flash, because you can't see the screen as to what mobile odin is doing. NOTE: "This is for mobile odin only" the PC way you can just go into recovery like normal holding the keys down. Not sure it matters if you wait the 10 seconds but I do just to be safe....again for mobile odin only.
4: Once in agats recovery just flash whatever zips you need to ie: modem.zip, toggles addon.zip, and whatever else you want to flash aside from a kernel.
5: once you are done flashing the zips, find the FK23 or FL04 kernel zip file and flash it.
6: go to the reboot system and click it and let it boot up. It should boot up like normal, only with whatever zip file you flashed IE: if you did a modem, go to system and check your baseband, if you had FL04 and flashed FK23 back, you should now see FK23 baseband listed, if you still see FL04 you did something wrong.
"Method2 - The PC odin way"
This way is assuming you have downloaded PC odin and have it installed already.
1: Start PC odin
2: Click the pda slot and select the file you want to use (normally a tar file)
3: hit start
4: wait for it to say done and turn green
phone should reboot.
"Method 3 - One click odin"
quite simple, just d/l the one click of your choice, click the one click exe file and hit start t the bottom.
Sorry so lengthy, but I just wanted to give more in depth info.
Hope this clarifies and helps out to understand a lil bit more