I think they're on par with each other from that perspective. According to the manufacturer, Clasico is their Bay Rum with the clove still in it while Atomic Age has the clove scent removed.
I have tried a few Bayrum soaps like Colonel Conk Bayrum(1st one I bought and enjoyed it a lot, old formula.)
Ogallala Bayrum & Sandalwood soap( nice scent with some clove).
Ogallala Bayrum sage and cedarwood soap( it's ok but not as good as the Sandalwood IMO.)
Bayrum Aftershaves
Ogallala Bayrum & Sandal wood( very addictive scent when it dries down a little for my self + on second jug. I like Bayrum splash for nice change once in a while from other scents. It does have some clove but the Sandal wood changes things a little for the better!).
Razor : Yaqi Excalibur SE 50mm with a Yaqi Milano 316SSP handle. Mfg 2021>, tame mid range. Simple blade clamping system and design. Small head parts are easier to assemble on a wash cloth for myself. Had a close comfortable shave this morning. Blade : Schick proline (6) sharp and smooth with reasonable longevity. Soap : TOBS herbal Sandalwood cream, very nice fragrance IMO with excellent lather qualities. Brush : Yaqi "Black marble" 24mm Tuxedo knot. Excellent lather generator, cloud like soft tips, nice splay scrubber + excellent lather painter. Pre shave : (Dedicated Cashmere synthetic)Brush wash whole face with CeraVe hand bar cleanser with a dollop of clear Aloe Vera on the cleaned beard area. Prep : Cold water rinse after each pass of 2 + pickups. WTG + ATG + pickups. Post shave : Ogallala Bayrum and sandalwood(2nd jug) + a dollop of Geo F Trumper Sandalwood skin food. Results : or CCS,DFS,BBs + no irritation + no weepers=
Had a close comfortable shave this morning with my Yaqi 50mm SE Yaqi Excalibur razor with a Schick proline.