If you want both of the stars to appear as sun like discs in the sky of a habitable planet, it is best to have the planet orbit both stars.
If you want both of the stars to appear with almost exactly the same apparent diameter in the sky of the planet, true twin suns, then the planet almost certainly has to orbit around both of the stars.
In a few cases of planets that orbit one of the stars and not the other in double star system, it may be possible for the two stars to have the right diameters and distances to sometimes line up so that they look about the same size in the sky of the planet for a short period of time, maybe a few percent of the total time it takes for the two stars to orbit each other, which can be many Earth years.
In your System A), a circumbinary or P-type system, where the planet orbits around the two stars, the planet will have to orbit at least 2 to 4 times the distance between the two stars. Both of the stars should appear as discs in the sky of the planet. As the two stars orbit around each other first the bright one would eclipse the dimmer one and then the dimmer one would eclipse the brighter one. And most of the time the two stars would be between eclipses and appear side by side in the sky. It is quite possible for the two stars to be separated by ten or twenty times their diameters, for example, and the planet to orbit at a distance of about 100 times the diameters of the two stars. Thus the two stars would appear clearly separated most of the time.
Your saying that the two stars would appear as one bright point in the sky in system A) is incorrect. A planet would have to orbit a type O supergiant or something for it's star to appear as a point of light in the sky at a habitable distance. And it is impossible for a type O supergiant star to have a habitable planet anyway, so that doesn't count.
As for your system B), which is called a S-type orbit, the farther star will not be much father away when it is on the opposite site of the nearer star than when it is on the closer side of the nearer star.
Suppose that the two stars have almost circular orbits around each other that are ten times the distance of the planet's orbit around the nearer star (Which is a bit farther than the minimum separation needed for stable planetary orbits. Thus the distance from the planet will vary between 9 times and 11 times the distances of the nearer star from the planet.
If the two stars have exactly the same diameter and brightness (and of course they do not have to), the farther star will seem to have between 0.0909 and 0.1111 the diameter of the closer star, and will be be between 0.0082 and 0.0123 times the brightness of the closer star.
Suppose that the two stars have almost circular orbits around each other that are 100 times the distance of the planet's orbit around the nearer star. Thus the distance from the planet will vary between 99 times and 101 times the distances of the nearer star from the planet.
If the two stars have exactly the same diameter and brightness (and of course they do not have to), the farther star will seem to have between 0.0099 and 0.0101 the diameter of the closer star, and will be be between 0.000102 and 0.000098 times the brightness of the closer star. Note that on Earth the full moon is only 0.00000025 times as bright as the Sun, so if the farther star appeared only 0.000098 times as bright as the nearer star it would still be many times as bright as the full moon on Earth and easily visible in daylight on the planet
Thus if the two stars have almost circular orbits around their common center of mass, instead of highly elliptical ones, the apparent diameter and apparent brightness of the farther star will not vary by very much. Your worry about the planet's orbit taking it much farther away from the farther star is not scientifically valid.
The big problem with your system B) with a habitable planet in a S-type orbit around only one of the stars, would be getting the two different stars to appear to have the same angular diameter and the same apparent brightness as seen from the habitable planet.
In your system type A), with the habitable planet in a P-type orbit around both the stars, both of the stars will be about the same distance from the habitable planet all the time. Thus the apparent diameter and the apparent brightness of both of the stars will have the same ratio as seen from the habitable planet as they actually have. So if the two stars happen to have almost identical actual size and luminosity they will appear to have almost identical apparent size and luminosity as seen from the habitable planet.
But in your system type B) with the habitable planet orbiting in a S-type orbit around only one of the stars, the farther star will have to be at least several times farther from the planet than the star the planet orbits. Thus if you don't need the two stars to have the same apparent diameter and the same apparent brightness as seen from the habitable planet, there is no problem. There are plenty of possible configurations that will have the farther star have a smaller apparent diameter as seen from the habitable planet, and also a much less apparent brightness, while still shining brighter than any star in Earth's sky or even the full moon.
But if you want the two stars in your system type B), with the habitable planet orbiting in a S-type orbit around only one of the stars, to appear to have the same diameter and the same luminosity as seen from the habitable planet, you will have a problem because one of the stars will have to be at least several times as far away as the other star.
In that situation it will be difficult to have the farther star appear to have the same apparent size as the nearer star as seen from the habitable planet, and it will be difficult to have the farther star appear to have the same brightness as the nearer star as seen from the habitable planet, and it will be just about impossible to have both.
You might be able to make the apparent size match, and you might be able to make the apparent brightness match, but it would be almost impossible to make both match.
If there is a habitable planet in your solar system, you will want both of the stars in your system to be main sequence stars. The size and brightness of main sequence stars depend on their masses. And if you change the mass of a main sequence star the size and the luminosity will change according to different formulas. You can never get the size and the luminosity to change in the same amount, so that the farther star will have both the necessary actual size and the necessary actual brightness to have the same apparent size and the same apparent brightness as seen from the habitable planet.
So in your system type B) with the habitable planet orbiting in a S-type orbit around only one of the stars, you will have to settle for noticeable differences in the apparent diameter and apparent brightness of the two stars as seen from the habitable planet.
