Neither of these builds a form. Both assume you have already written one, and both take over at the moment somebody presses submit — validating the data, filtering the spam, emailing you the result and keeping a copy you can read later. Choosing between them is not a question about features, because the features are close. It is a question about what each one does when a plan runs out.
What happens when you hit the limit
This is the real difference and it is worth understanding before a campaign rather than during one. Basin keeps collecting past the monthly cap. Submissions above the allowance are still delivered, and the excess is billed by the thousand on a published scale that falls as volume rises — starting at just over five dollars per thousand and dropping to two at the top. Nothing switches off, and nothing is discarded.
Formspree's plans are ladders instead. Each tier carries a fixed monthly allowance, from fifty submissions on the free plan up to twenty thousand on Business, and moving beyond one means moving up. That is more predictable and less forgiving: you always know the bill, and a form that suddenly succeeds is a form that needs attention.
Basin also excludes filtered spam from the count, which matters more than it sounds. A form under attack can otherwise burn a monthly allowance without a single genuine submission arriving.
What happens to the data afterwards
Here the two are closer, and Formspree has the slightly longer reach. Both offer an API for pulling submissions programmatically, both filter spam automatically, both accept file uploads and both connect to the usual automation tools without code. Formspree adds routing rules that send a submission to different addresses, flag it, or change where the visitor lands afterwards, based on logic you define — a small amount of decision-making in a product that otherwise does none.
Both are equally silent on appearance, which is the point of the category. The form is your markup and your stylesheet, so how it looks and how far it bends are decided entirely by you.
Which should you choose?
Choose Basin if the volume is unpredictable and losing submissions would be worse than an unexpected invoice. Campaign landing pages, launch forms and anything seasonal fit here, and the published overage rate means the surprise has a known ceiling.
Choose Formspree if you would rather know the bill in advance and treat the cap as a signal to upgrade. Steady contact forms on a site with predictable traffic fit that shape, and the routing rules are worth having if submissions need to reach more than one place.
If neither free tier is large enough to evaluate properly, a third option with a bigger free allowance may serve better than paying to test either of these.

Formspree
Point your own form at their endpoint and stop thinking about the server.

Basin
A form backend that keeps collecting after you pass the plan you paid for.
Specs
Ratings
Ease of building
How the form looks
The form is your own HTML, so there is no vendor design to score. This 1 marks the dimension as inapplicable rather than the output as poor.
Basin receives a POST from markup you wrote and styled yourself, so nothing here is the vendor's to be judged on. Read the 1 as not applicable.
How much you can change it
Logic and question types
What happens after submit
Value for money
Features
Pricing
Formspree
Basin