I agree with this but my only problem with Legendary is it just scales. So your initial start is rough. So its definitely harder, but you get to a point, more quickly then not in my opinion that it feels like Master difficulty without crafting. I mean this is my opinion, and it depends on what build your playing. My point I guess is Legendary over all is more hardcoe, and more difficult. However its also more of a time sink. Which is great, I love Skyrim, I do, but they REALLY should have put Legendary difficulty in sooner. I just can't be bothered anymore to mess with crafting in the game. I like to setup my game to be challenging and yes DiD, but avoiding any crafting, personally. Its definitely a easier road initially, but you guys might enjoy no crafting on Master to still have that challenging experience without the time sink.
Then again you guys might hate it, my thing is, once I get to a certain point on Legendary with crafting, I am playing on Master with no crafting, if you know what I mean. Initially its a mother [censored], which is great for competitions like you guys do, but man you guys are like at this point that, honestly one of you is going to haft to make a really dumb decision to die, but that is my opinion. Over all having to build up crafting in Legendary is part of the difficulty as well, I feel like you guys beat the game though already, you tied with each other. If someone dies now someone was doing something really dumb.
Then again, there are powerful enchanted items throughout the game, you can set rules around it, but anyway, I was just giving my perspective on your all's competition. Its at a point in my opinion that you guys both won, level 45 on Legendary with your all's rules, that is winning. You guys keep doing your thing though, its all about fun, and maybe you guys are trying to hit level 81 for all I know without dying.