but in general, which of these approaches requires you to carry more extra
weight on launch?

For a given payload, a winged spacecraft weighs a minimum 15% more, and
typically 50-250% more.

(see http://www.abo.fi/~mlindroo/SpaceLVs/Slides/sld017.htm )

A capsule/DC-X vehicle has all acceleration loads in the same direction,
and the CoG in a favourable location.

But there is no free lunch.

A capsule with a parachute (the absolute lightest) gives up the option of
landing if weather is bad.
If returning to runway it needs wheels, if simple ones.
If splashing down it requires flotation gear (and a retrieval ship).

The DC-X is better off (retro fuel proabably weighs about the same as a
parachute), but the heat shielding becomes more complex. For a mature
technology and Return-on-demand missions the DC-X comes out as the lightest.
It does require nerves of steel - if the ship fluffs the retro burn at 5000'
AGL and 300kts, in 10 seconds you go splat!