I've never tried the Bighorn action, it was always out of stock when I was building a new custom rifle. But, they are a nice action. I've built four rifles with custom actions, they all accept Savage style pre-fit barrels.
My first was a Shilen DGR action, it is made by Stiller for Shilen and it actually uses the same style bolt head as Savage. It's a nice smooth action, but there are better choices for the price.
Shilen DGR action, Shilen select match 26" 6.5 CM barrel, Trigger Tech Special trigger, KRG Whiskey 3 chassis, all metal cerakoted in burnt bronze, 20moa rail, ARC M10 rings holding an IOR Valdada Recon 4-28x50 scope.
My next was an American Rifle Co - Nucleus action. ARC makes some damn good actions! Smooth as glass, controlled feeding.
ARC Nucleus action, X-Caliber 20" 22 CM barrel, Trigger Tech Diamond trigger, KRG Bravo chassis, 30moa rail, ARC M10 rings holding a S&B PMII 5-25x56 scope
ARC - Nucleus 2.0 action - An upgraded action over the original, I like it.
ARC Nucleus 2.0, Rock Creek 20" 223 Remington barrel, Trigger Tech Diamond trigger, KRG Bravo chassis, 30moa rail, ARC M10 rings holding a S&B PMII 5-25x56 scope
Last up is the ARC Archimedes action. I don't know if I'll ever need the pivoting bolt handle to help with a stuck case, but that is one of the upgrades that Ted invented for this action. All of my ARC actions are fantastic.
Arc Archimedes action, X-Caliber 22" 25 CM barrel, Trigger Tech Special trigger, Woox Exactus chassis, 30moa rail, ARC M10 rings holding an Athlon Cronus 4.5-29x56 scope.
There aren't many negatives when it comes to building off a custom action. They are so much better operating than a factory action. The positives of using them over a Savage action is the vast choices you have in parts that you can buy since most custom actions share a Remington 700 footprint. I don't regret building any of mine.
