in my area the unit should come on around 10 am
and run until 9 pm in the heat of the summer.

long run times remove humidity.
less RH and the air feels cooler because the
humidity is removed.

short cycles- shutting on and off
reduce humidity removal, increase operating costs
(costs less to turn on and run than on and off)
and shorten life of system.

you don't say how old your system is or
the efficiency (seer).
10 SEER to 13 SEER is a good savings.
this is why the hvac industry jumped from
10 to 13 SEER as minmum produced.

13 SEER to 15-17 SEER is a good savings.

if ductwork works well now, and provides sufficient
temps then if new unit is correctly installed
then temps would not be lower.
if two stage equipment is installed with fan
set in low speed, then the air delivered would
actually be colder.

new unit would consume less power.

best of luck

sounds like something is wrong with your present system, have you ever had it maintained?

Vent temps are ok. 12-14f diff? Cannot recall. Did service last year. Took off sheet metal exterior and vacuumed condenser and washed out fins. Ugh. Fun job. Louvers really bite for cleaning. Unit is 37 yrs old. Jokes on me I suppose. New unit would have paid for itself in elec savings yrs ago.

"12-14f diff? "

Should be larger.

"Unit is 37 yrs old."

Not worth much besides replacement or simple repairs.

Checking charge would be a first step.

37 yrs old I would bet you will never have a system last that long again but it needs to gooooo.