Originally? No. Halo takes inspiration from Marathon more than anything, which took inspriation from Doom. Marathon vs. Doom would be a more accurate comparison.
But to get into specific points:
They both are hailed as some kind of messiah in thier games
Not really. Doomguy didn't have the messiah thing going until Doom 2016. And John's never been treated as a messiah. The Spatan-IIs were given a certain amount of reverence, but John never got more than any of the others outside the program, even if he was their de facto leader.
as they save humans from Demons/Aliens.
You've just described 90% of FPS sci-fi.
When Doomguy Shoot Demons, Haloguy Shoot pokemon looking aliens.
Um...
both have thier own signature weapon like shotgun and assault rifle.
That's a stretch. The shotgun didn't become a signature weapon until Doom 2016 at the earliest. meanwhile, John's never had a signature weapon. Yeah, he has an assault rifle on most covers, but that's a stretch.
when we look at games, the concept is similar. Alien invasion/Demonic invasion, saving humans from threats.
Again, that's an insanely broad plot point.
I feel like Halo either is heavily inspired by Doom or just rip off.
Again, see Marathon. And Doom was already ripping off Aliens.
Doom series basically evolved yet Halo is combat devolved now with infinite looking very outdated.
The Doom series did evolve, I'll grant you that. I'll also grant that Infinite looks outdated. But this isn't to say one ripped off the other.
Masterchief and Doomguy are exact same characters imo.
Except they're not. Sure, they've got some generic similarities (supersoldiers), but look up their bios, there's a tonne of differences.
I feel like Halo either is heavily inspired by Doom or just rip off.
Doom series basically evolved yet Halo is combat devolved now with infinite looking very outdated.
Masterchief is space marine so is Doom guy as he was original.
The space marine archtype goes at least as far back as Starship Troopers. Again, this is so broad a trope it's meaningless.
Doomguy lable as the choosen one who destroy demons. so is masterchief although he fought with other marines.
Doomguy didn't become a "chosen one" until Doom 2016. And again, John's never been given any religious reverence - certainly nowhere approaching the same scale.
There wont be a Halo without Doom.
That's technically true, if we assume that if Doom never existed, no other game like it would have been created. But again, that's broad. Doom would never exist without Wolfenstein. Wolfenstein would never exist without the PC. The PC would never exist without...well, so on and so forth.
There wont be Masterchief without Doomguy since masterchief is inspired by Doomguy.
Again, that's a stretch. The space marine archtype predates Doomguy. And John owes more to Mjolnir Recon 54 than Doomguy.
If this was a Marathon vs. Doom comparison, this would be different, but it isn't.
Anyway....No B-Cell not a chance. Halo is worse than doom in every single way.
Better characters, better story, better setting, better themes, basically anything related to the Five Pillars of Story for starters.
If we're talking about gameplay, that's a different matter. I'd still say Halo's better overall, but at this point in time, I'll concede that Doom is better. The last Doom game was Doom Eternal, which was awesome. Infinite, on the other hand, looks lacklustre. And as much as I enjoyed Halo 5 (and to a lesser extent, Halo Wars 2), I'd still put Eternal above them.
Honestly, a lot of Halo's 'stuff' can be traced back to a specific series of 90's FPS, Marathon, and its sequels Marathon Durandal and Marathon Infinity.
Being guided around by various AI, one of which is a bit crazy and has its own agender.
Being a power armoured and enhanced superhuman who is the only one to save the day.
A strong narrative focus.
Enemies who are an alliance of races being forced into cooperation by a single overlord race.
Created for Mac's by a little developer named Bungie. Maybe you've heard of them?
Thank you!
Look, I can't claim to be some kind of retro fan or anything (I only learnt about Marathon through Halo, and I've only played through M1 and some of Durandal), but Marathon's a far more important evolutionary link to Halo than Doom, even if Marathon stems from Doom in a gameplay sense.