Outside is better at stopping water reaching the structure; inside is better at being possible. Around a crawl space the outside route is usually shallower and cheaper than around a basement, which shifts the balance toward exterior work — unless access is blocked by a patio, a deck, a driveway or a neighboring wall.
What the ground under a crawl space here is doing
The shallowest mapped seasonal water table in Syracuse is 3.1 inches down and up to 100% of the mapped soil is rated as susceptible to ponding. A crawl space floor sits close to both. On this ground the water arrives as liquid from below rather than as vapour from bare soil, which rules out the cheap answer: a sealed ground barrier will trap it rather than stop it. Interior collection and a sump is usually the honest design here, whatever the outside access allows.
The reasoning behind that
An exterior drain intercepts water before it reaches the structure. It is the more complete fix and it costs what excavation costs. Around a crawl space the footing is shallower than a basement’s, so the trench is shallower and the price gap narrows.
An interior drain collects water that has already arrived and takes it to a sump. It does not keep the ground dry, but it is installed from inside, which matters when the outside of the wall is under something that cannot be dug up.
For crawl spaces specifically there is a third thing that is not drainage at all: a sealed vapor barrier across the ground. A great deal of crawl space moisture is evaporation from bare soil rather than liquid water arriving, and a barrier addresses that for very little.
Diagnose which of the three you have before choosing. Liquid water after rain is drainage. Damp with no visible water is very often vapor.
More on this: Interior vs Exterior French Drain in Syracuse, UT.
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