Plus and minuses to both perks really. Cowboy has a good range of low and high level weapons and a selection of high dps and high damage weapons (the latter for that extra punch you need to deal with high DT critters like giant radscorpions and BOS paladins). Down side is it costs a lot more skill points to get the perk (45 Guns and 45 Melee) not to mention the points you have to pump into Lockpick to get Lucky, arguably the best weapon covered by the perk. Plus side is, with the Handloader perk, you get crafted ammunition that boosts the damage of all but one of the weapons covered by the perk (That Gun is the exception) even further than the 25% from Cowboy itself.
Grunt has some excellent dps weapons (even a 9mm SMG with a light bolt and Grunt is insane dps for the level you can get it) but for the high DT targets you have to rely on Grenade Rifles/Launchers and to max out those weapons you need to put 3 perk levels into Demolition Expert. Also, unlike Cowboy, you don't get as many Handloaded ammunition options (.308 for the light machine gun and .45 for the pistol/smg only). Plus side is you can find Assault and Marksman Carbines placed in the world if you know where to look and you can get A Light Shining in the Darkness for completing a few hours of Honest Hearts content that you'd do for the experience anyway.
Personally I take Grunt at Levl 8 when it becomes available but wait into the teens to take Cowboy, when I can spare the extra points for Melee and Brush Guns start to become available from vendors,
Now if the question you were asking isn't about the relative merits of the perks but what I prefer to roleplay then I guess I'm not either. More of a Rubble Rat. Give me a modded varmint rifle and a tire iron and those are my happiest levels. But then I always like the slingshot and rusty pocket knife levels in rpgs

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