Overall, the handling of a _good_ randonneur bike with a front load
and wider tires is remarkably similar to the handling of a racing
bike with no load and narrow tires, as Phil mentioned. That is the
beauty of a _good_ randonneur bike, as you get the speed of a racing
bike with added versatility.
Both have steep angles (usually 73 degrees), but the randonneur bike
has much more fork rake. There are some minor handling differences as
you approach the cornering limit, which you may or may not feel:
– the racing bike reacts more to leaning, because it has more wheel
flop. It reacts more quickly to your input. The bike first falls into
the curve, then goes straight after you “caught” it, rather than
cornering on a constant radius. This is great for 90-degree turns,
for example, in criteriums. Hairpins are a bit more “hairy,” because
you’ll have to correct more to keep the bike on a constant radius.
– the randonneur bike is steered more into the corner, but once you
are cornering, it will be on a more constant radius, yet easily
adjusted. Hairpin turns are easy, whereas a criterium would be more
difficult, as the bike does not react before you do. Basically, you
set up the bike for the corner. The randonneur bike handles more
precisely – you could hit a quarter lying on the road in mid-corner.
– under a tired rider, the randonneur bike will be more easy to keep
riding straight (reacts less to leaning).
By the way, most classic racing bikes before 1965 had a “randonneur”
geometry, because they were designed for long races over challenging
courses in small groups, rather than riding in a huge pack jostling
for position. (Tires were wider, too.)
The mechanics behind this and the exact geometries for various tire
sizes, etc., have been discussed in Bicycle Quarterly, most recently
in Volume 5, No. 3 (“How to Design a Well-Handling Bicycle”).