Strange, I've had a very different experience.
On my first playthrough of FWE, I made it to about lvl 14 before running into a quest-breaking bug and taking a short break from FO3 as well as deciding to just start from scratch. Fresh install, all that jazz. I had Speech, Lockpicking, and Small Guns tagged, and I tagged Energy Weapons at lvl 14 to make use of the plasma rifle I'd found (which, honestly, was hella underwhelming as a weapon compared to laser rifles.) I'd played through with all of the DLCs installed, so I was rocking Winterized T-51B Power Armor for most of the game (though I'd switched to the Prototype Medic Armor when I found it in Old Olney) with a base DR of about 59. I believe I had 6 END, so I had something like 225 HP (this is just under roughly half of the HP I had in vanilla, which was about 510.) By that point, raiders were a mostly minor threat (befitting the low XP), though Ramboing in usually still got me killed if they were packing assault rifles and there were more than a couple of them. Super Mutants were about the same... mostly just an annoyance, but a large group of them (especially if they had FN FALs or M60s) could be a huge threat if I wasn't careful. Ironically Deathclaws, Yao Guai, and Wanamingos were almost nonthreats due to the Dart Gun being almost ludicrously overpowered (-1000 to both legs with one shot is a little... excessive.) At any rate, I enjoyed it - while power armor made it much harder for me to die, it didn't render me invulnerable. I suppose if you're looking for the Rambo experience vanilla provides, you'll be disappointed - I played a no-Sneak melee character on my vanilla playthrough and I could literally just wade through entire packs of super mutant brutes and masters and maybe use one stimpak the whole time, soaking bullets up like a sponge... and I wasn't even in power armor.
I'm now playing through FWE as a no-Sneak melee character (also with Energy Weapons instead of Speech this time) and I'm not using any DLC except Broken Steel, since I felt walking out of Operation Anchorage with power armor and great weapons was a little cheesy and neither The Pitt nor Point Lookout are that fun. I'm currently rocking about 210 HP at lvl 4 (7 END) and I'm at about 19 DR... and I can tell a major difference in how much damage I take, even though my HP values are mostly the same. But even so, the game mostly plays about the same - I usually use a gun to pick off the most dangerous enemies first (with my low DR, that's basically everyone except stragglers or people I've crippled) and then finish them with melee. I also have a decent Explosives skill, so mines and grenades are also a major part of my gameplay plan. FWE (and especially if you're also using MMM and the Increased Spawns esp like I am) requires more thought and planning in your game, and that often does mean more frequent quickloading, especially if things go sour (like a nade bounces off of thin air because the Gamebryo engine svcks.) Still, I enjoy it. While I'm not swimming in them, I do have enough Stimpaks to get by (I've got 5 now... on my previous playthrough, I was carrying more than 100 after completing Point Lookout, where I swear to god they're everywhere) and I also have enough Morphine, Aspirin/Ibuprofen, and Buffout to survive the harder fights. Expect to be using chems a lot in FWE, especially early on. I'm also using STR+END based healing on rest, and I can regain about a third of my HP with two hours of rest, and almost all of my HP with six. Obviously, this doesn't take care of being crippled... but that's what the Wasteland Doctor and Wasteland Surgeon perks are for.
If you're repeatedly failing a battle, try tackling it at a different angle. If possible, set up some mines beforehand and lure your enemies onto them. If you have cover or corners to take advantage of, grab your enemies attention and then throw nades around the corner. If you've got good Sneak, sneak around and use the autocrit bonus to instantly kill weaker enemies before they know you're there. Don't be afraid to use chems - there's a reason there are a skillion new chems in FWE. Morphine and Ceremonial Herbs should always be carried in case you get crippled and aren't in a position to use your triage. Aspirin and Ibuprofen add that little bit of extra DR that can make all the difference, you can't get addicted to them, and they're cheap. Tribal Healing Powder heals a pretty decent amount of HP for its cost, and Multivitamin Pills could be considered to be Buffout Lite (and without the chance for addiction.)
FWE ain't the mod for you if you're wanting to Rambo around like you do in vanilla. At no point will you be a god squishing cockroaches - even the lowliest raider can kill you in a few headshots no matter what kind of armor you're wearing, and that's a good thing. You also have to consider that raider probably won't be as accurate as you, and sure as hell doesn't have the HP or DR you've got. Frag grenades and frag mines are both powerful and plentiful - invest some points into Explosives so you can make good use of them, because they're one of the greatest equalizers, especially in the early game. A couple of well-placed mines can prevent you being flanked and can easily kill melee enemies, and some well-placed grenades can wipe out entire groups of enemies. With 35 Explosives, a single frag grenade will routinely kill at least two raiders and at least cripple two more. There's some risk involved in using them, but what's life without risks?
Also, pick up Dogmeat at Scrapyard as soon as you can find the time to head down that way (I find it best to go there on your way to Minefield for Moira.) He's not invulnerable like he was in vanilla, but he's still a useful distraction and sometimes just drawing one gun to himself and off of you can make all the difference.
Oh, and on the subject of radiation... it's fine. Rad-X is hardly rare (not to mention Sativex, which can be used in place of Rad-X in a pinch), and RadAway isn't very rare, either. If you find yourself running around in irradiated areas or swimming in water a lot, consider investing in a Radiation Suit. With the exception of Point Lookout (which fairly svcks anyway), most water areas can be avoided in the capital wasteland by taking the long way around.