Play with the following variables. These are the numbers I run with and my system is like 3 years old. Video card is GeForce 8800GT. Don't know if that tells you anything.
iShadowMapResolutionSecondary=4096
iShadowMapResolutionPrimary=4096
iShadowMapResolution=2048
iShadowMaskQuarter=7
fInteriorShadowDistance=3000.0000
fShadowDistance=3000.0000
FYI:
It seems to me, that after 1.5, iShadowMaskQuarter no longer is a relevant parameter. Whatever you set it to (or allow the launcher quality presets to set it to, like 3 in case of Low or Medium) it reverts to 4, or at least that value is updated into the ini file (unless it is set to read only) by the game engine. Experimenting with it in 1.4 seemingly changed which marginal pixels on the shadow's edge would or would not be part of the shadow. That effect seemed to be random-like rather than having any clear pattern, and I would say that any claim that a specific value would sharpen the shadows (or something) could perhaps be illusory or a question of pure chance in a specific instance.
And by the way, I also have an 8800GT (with 1024MB VRAM). But anyway, I think the shadow settings are likely to tax the CPU rather than the GPU. I am running a dual core, 2.6 Ghz, socket 939, AMD FX-60 from several years ago (I don't even remember how old it is).
I would start by maxing out iShadowMapResolution at 4096 (as in Ultra; apparently this setting more or less controls the overall amount of resources committed to shadows and generally improves their resolution), and keeping it there (going any higher would be detrimental, unfortunately) if your CPU performance allows it (which it should, unless it is really marginal). Then experiment with the other parameters. I personally like having fShadowDistance at 5000 (this essentially determines how large the area is over which shadows are calculated, and increasing it creates shadows further away from the player but because it spreads out the shadow pixel map, it decreases the effective resolution that is achieved locally), and iBlurDeferredShadowMask at 3 (not included in the list above, and controls blurring of the shadow edge), but that is a question of taste. With these settings I also seem to have reduced or no exterior shadow striping without having to adjust fShadowBiasScale from its default.
P.S.
Also keep in mind, that real life shadows are seldom sharp. I stand 190 cm tall, and when the Sun shines at a 45 degree angle, the shadow of the top of my head on level ground is blurred over a distance of 2.5 cm, because the sun is not a point source of light, but a disk with a diameter. A tree branch at the height of 10 m would have to be several cm thick to leave any noticeable shadow at all.