Speed, ignorance of degrading like fragmentation, robustness, physical size, power requirements, heat creation, sound generation.
To elaborate:
You’d be hard pressed to find a SSD slower than around 4 times the speed of even the fastest HDD. Most (these days) are 10s of times faster.
SSDs just don’t get affected by fragmentation at all, while it’s the bane of HDDs - so the more you use the drive the less speedy it becomes (while with SSD it doesn’t matter how fragmented - it’s still the same speed). Of course using some file systems like EXT4 / BTRFS / etc. alleviates fragmentation, let’s face it most still use fragmentation prone file systems like FAT / NTFS - say thanks to Microsoft for that.
Drop a SSD on the floor and it will still work. Do so to a HDD and all your data is lost as will the drive be completely useless.
A SSD can easily be much smaller in physical size than a HDD, especially if you consider same capacities. The only reason some older SSDs are the same size as the HDD they’re replacing is because they need to get mounted into the same slot - most of the space inside is just air. But with things like M2 mounts you can see all they need to be is a card (around the size of a credit card).
The SSDs tend to use less than a 1/10 th of the power that a HDD does, so stuff like battery life gets extended. If you go with an economical HDD like a WD Green, you then loose even more speed, and usually also compromise on robustness, longevity and / or sound generation.
Due to less moving parts and no mechanical whatsoever, there is no friction - i.e. one less source of heat.
SSDs are completely silent, while HDDs always generate vibrations, motors spinning up and even scraping sounds.
The usual “fear” against SSDs is write-life-cycle, though in all cases HDDs tend to actually perform worse. That’s due to them constantly breaking because of their mechanical movement. Causing things like wear on their moving parts. At present SSDs tend to last about the same to slightly longer than similar HDDs - do some web searching on life expectancies of SSD vs HDD, you’ll be surprised to see the empirical test data.
The only benefit HDD has over SSD is cost - if you compare similar capacities. I.e. a 1TB HDD tends to be cheaper than a 1TB SSD. If you compare against things like life expectancies then the pricing is much closer - e.g. a server grade HDD is about the same cost as a SSD of the same capacity (while their expected life - measured in how many times they’re overwritten - is about the same).