Here are a few things to consider :
Tactics
If a full attack is "all" it takes to down someone, force Move actions. Could come from cover/concealment or combat maneuvers like Trip/Knockdown or Disarm. If you just play "rocket tag", you're implicitly accepting that if you miss, there's a good chance you're dead.
Note that this is exactly what happens IRL between powerful forces in a battle and in this respect, is not a "bug" of the system but a simple truth.
Intelligence
So you're targeted by a Master Ninja, who manages to sneak up on you and place a Death attack. Curse you, Hayabusa ! Wait, you made your save ! Time to grab your trusty bow and fill him with arrows...
Well, boo. The ninja has broken/stolen your bow as well. Not only does he make his escape, he's slowed you down by forcing you to have it repaired / replaced while you try to get it back.
This goes a step further in Tactics, and is to be expected of Ninja, for example. Study your target. Know their strengths and weaknesses as well as yours. "That Brilliant Bow of Badassitude could be a problem if I must escape. Can I get rid of it ? What about impairing the bowman ? Maybe I could blind him ?"
As an aside, the GM should make sure the players don't feel cheated though. Extreme competence is assumed as part of the characters (especially past level 10) and robbing them of that can be frustrating to no end for some.
Numbers
So they can take the Big-Ass-Monster down in a round ? What about 10 Medium-Sized-Nuisances ? One by itself could barely hope to hit them, but with flanking, teamwork feats and simply being all over the place, the little pests could prove to be annoying. Add in a Leader-type and you could even be worrying your characters.
Story happens
Take the characters down a notch or two through Story. Have them stripped of Rank and Privileges by the King or even make them straight Outlaws. Have them stranded on an island (and some of their equipment lost to the sea) after their boat got caught in a storm. Have their home base attacked (and their Mentor killed, leaving them unable to progress in their main class) while they were on mission.
Change focus for a while
Once all is said and done, if the combat has become so easy it's boring, it may be time to try a little courtly intrigue for a change. Or why not a mystery ? Possibly meshing with "Story happens" above, there are plenty of opportunities to take the players / characters out of their comfort zone while staying true to the setting. They'll be happy to resume bashing heads once they've stumbled for hours finding a tangible threat to pounce on. Or hey, maybe they'll actually enjoy trading piques with the Jester and decide they want a piece of land and a throne of their own ?
Pre-warning - I have little experience as a DM dealing with difficult players, but I'm getting pretty used to dealing with difficult tables in general.
A couple of things we found really handy for our horde of uncooperative players:
Talk it out / Remind him
You said in the comments that:
I have talked to him about it before. He seems understanding until a situation occurs where it basically sets it off
So he may just need a gentle, at table reminder about the discussion you've had. A simple prod in the right direction might be all he needs to cool his head. DnD can get pretty intense at times, and it could just simply slip his mind as he gets into it.
Players really getting into your campaign is what you want as a DM, as long as they're getting into in good spirit.
Is the table okay with this behavior?
Is it just you that's bothered by this? How your table reacts to his behavior could also dictate how you handle it.
During our romps with difficult players, one player refused to cooperate with the DM to the point we almost had to kick him out. But the DM pulled me aside, and asked me to respond to every that player said as in character.
If your brother is heavily into role playing, responding in-kind and keeping it to your characters may help stem the OOC poor behavior.
I.E - If he's complaining about the Gods not lending a hand, a NPC (or other player) could take that at face value. "[Gods Name Here] wouldn't care about a single [town/city/country/]! Our lifes are nothing compared to the grand scheme of things. The immortal plane is beyond our understanding..."
If all else fails, are you guys that right group for him?
You also said that:
He generally seems much kinder to other dms, doesn't have the remarks or throws tantrums to them. (He also is my older brother)
So it could very much be as simple as -Younger brother has to do it my way rawr- or that the tables play-style and campaign just doesn't fit him.
Saying that you play to his level, but then having a level 15 player challenge a lv 20 NPC, says to me that maybe he doesn't want that much of a challenge.
He could be looking for something a bit more cruisy, or maybe he just really really wanted to play pirate captain.
But either way, if you can't find a middle ground with him, maybe have another look to see if he matches your table. It could be as simple as a few small tweaks to the campaign to keep everyone happy.
Best Answer
I have never tried this in GURPs, but I have played other games where there were large discrepancies in the starting powers of the characters. I have tried mixed old World of Darkness games with different species and different versions of DnD with widely separate starting powers (in fact, this almost happens naturally in later versions of DnD if you have skilled optimizers next to non-optimizers) and a few others.
Generally, it has been my experience that widely different power levels do not work well together. Someone will end up feeling overshadowed or someone will end up carrying most of the load, and it makes the campaign very hard to design for from the GM's perspective.
I know of two exceptions where it works quite well though.
For a new player, especially if they are a guest.
If you have an existing campaign going and you are bringing in a new player, especially someone who is new not just to the campaign but to roleplaying in general, then it can make sense to make them somewhat more powerful than the others. This makes it easier for them to have a chance to shine and it makes things more "fault tolerant" since the character has enough power to survive novice player mistakes.
I'm not actually recommending this as it can cause problems down the road as that player becomes more comfortable with role playing but still has the strongest character. But it can help introduce someone to roleplaying in a positive way, especially if that person is a guest that won't be able to play through the whole campaign or if it is meant to be a short campaign anyway. I've been on the receiving end of this when I was much younger and a new player and it was quite pleasant for me.
If someone wants to play a weaker character for narrative reasons.
I like gishy characters (fighter/mages). I will take a gishy character even if I know full well that it is suboptimal, as long as its not so suboptimal that I expect it to cause real problems in the power level.
In World of Darkness, the character types are not all made equal. Mages for instance tend to be more powerful than vampires and everything is more powerful than ghouls. But some people will knowingly take a weaker character type because they like it better. As long as the power discrepancy isn't so big that it will cause problems and as long as the player realizes what they are doing, this can work very well and keep everyone happy.
In general
In general, I really think the power levels should be close to equal. There are some exceptions, but those exceptions work best when the differences are small rather than huge and when everyone at the table understands what is being done and agrees to it.
I haven't played GURPS, but that looks like a pretty big power spread and I'm not sure how well it would work.