Are there any iron sights that give similar or better target acquisition time and field of view, compared to red dot sights?
Preferably not BUIS.

I don't think so cause no matter what you still have to line up two sights, and focus on your front sight at the same time. Iron sights wont be as fast to my eyes. YMMV and point shooting is a different thread.

Open-type "express" sights will be faster than peeps.

You will never get irons that are faster than RDs.  I really like carry handles and I tried to run one as my primary for awhile and it just isn't as effective as optics.  If you are using irons, you must somewhat focus on the front sight post (as you are taught) and, for me at least, takes away some of my focus on my surroundings.  With something like an EOTech or aimpoint, you can focus out on what you are looking at and the reticle is projected out on your target.  I have found that if I try to focus on the target with irons, the post blurs significantly.  I would think that at close range, you can definitely be quick with irons but due to the way they must be lined up, there is a much smaller margin of error when it comes to bringing your rifle up to your line of sight (and it will never be as fast as you could be with an optic).  If my optic goes down in an HD type situation, I wouldn't even deploy the rear sight... i'd put the FSP in the middle of the window (absolute cowitness) and simply use the front sight.

With practice, irons can be about as fast as a red dot at close range.  Many people will disagree, but this is my experience after running both back to back.  Most of the time in CQ is spent physically manipulating the rifle, not fine tuning sight picture.  With irons you need to sort of trust your instincts to go fast.

Most people are going to give up a little accuracy or speed with irons over a red dot, but it's surprising what you can do with some training.

As for what type, I use A2 style sights on my irons gun, but with a thinner national match front post and a ghost ring for speed in the rear.  Never tried pistol style sights on an AR.

At extreme close distances, point shooting is the fastest.  A sometimes overlooked feature is that, besides speed, RDS give you low light capability.  

No matter how much you train, RDS will still be faster.

This is true with a lot of training.

If you took all that iron sight training and spent it doing RDS training, you would still be faster with the RDS.  

Iron sights will never catch a RDS on speed.

Nothing's as fast as a dot, but fiber optics come close.

CQM with irons isn't all that hard with lots of practice. Use the large aperture of the a2 rear sight, and once the target is generally lined up you will hit it. But irons are less than ideal when shooting from positions of disadvantage, low light, and while wearing armor. Red dots reign supreme for a reason.

honestly its all about training and muscle memory. sights dont make you a better shooter.
know yourself and know your weapon.

as far as pistols go i take the sights off of it as soon as i get home. as a carry pistol i train by bringing the pistol up naturally taking two shots and bringing it back down to see where the pistol hits on my natural aim
150+ rounds later i can hit the center of the paper in 3 in groups at 25 yrds.

rifles require a bit more precision but the same concept applies. bring your rifle up to your cheek weld and shoot without looking down the sights. its muscle memory. eventually the red dot will be a reference and in a real life HD or combat situation
you will be confident you can hit the target

NOTE
i am not saying bring the rifle up and shoot at 50m+ your groups would be all over if you even hit the paper
this is CQC and is a training technique from 7 to 25 meters

To the OP, I want to be the first in to tell you to disregard the above advice about "sights don't matter".  

It is the Indian AND the Arrow.  

P.S.  On a related note, I emailed the US Military to tell them they don't need their ACOGs and Aimpoints anymore.  I expect them to get right back to me thanking me for my cost saving suggestion.