Since the question was originally for the SE-210 . I shall answer for that type aircraft.
The Caravelle I, I-A, III, and VI-N (all powered by RR Avon RA-29) had drag chutes.
The Caravelle VI-R (still with RR Avon) had reversers, no drag chute.
Later Caravelle types, 10R and 12 etc. had P&W JT8D engines with reversers, no drag chutes.
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Operations notes -
Drag chutes were required for short or wet/slippery runways - often as per operations policy.
If I recall correctly, the crosswind limit (policy again) was reduced by half.
Recalling also a policy to wait for nose wheel touchdown before deployment in crosswind.
Caravelles often carried a spare drag chute canister ready to be installed after the use of the installed unit, if considered MEL item.
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To keep the drag chute "UP" (preventing it to fall in dirt), keep some power on engines, until reaching point of chute release.
Operating on a wet runway with drag chute use is not fun. Worst case scenario was (at times) requiring the F/E - there were F/E in SE-210 - to get the wet/dirty drag chute, in their shiny-clean uniform. In the Lear, pick-up is always the responsibility of co-pilots (now we know why these guys need a type rating and ATPL).
Therefore use of drag chute was often "avoided" - with resulting incidents and accidents.
If drag chute use required, it should be used "AT ONCE, ASAP after touchdown" since effectiveness is by the square of airspeed.
But pilots avoid using drag chute as requited (clean uniform disasters) so the drag chute is kept un-deployed as long as possible, until our superior P-I-C realizes it is necessary to use it... well, then is TOO LATE. At reduced speed, the drag chute is as effective as a piece of wet Kleenex tissue.
There was such incident of a Sobelair SE-210 at Innsbruck. Ended 200m beyond end as drag chute deployed too late = Captain said "I wanted to avoid to have to pick the chute" - Valid excuse and superior airmanship...
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In a Lear (24-25) the drag chute weighs some 25 lbs, the Dee Howard reversers weigh 350 lbs...
If used properly, drag chute is reported to be much more effective than reversers.
In the Lear, use of reversers in conjunction with drag chute use is prohibited...
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Happy contrails -
Enjoying my retirement (what is an aeroplane...?) - Did I spell that word right...?
Getting back to my rocking chair... Cheers -
BelArgUSA