Jump does not let you bypass the 'Speed' restraint on jumping. But the ring is still useful
As to Jump (and the boots) not increasing your speed, here is some Developer commentary on the matter, specifically addressing these effects.
Question posed: "Can you jump farther than your movement when using magic i.e spell Jump & boots of striding and springing?"
To be clear, things like the jump spell don't increase speed. You can jump crazy far, but your speed caps it. -Crawford
Are you saying you can't jump farther than your speed even with Jump spell or Boots of Striding and Springing? -Followup Question Asked
Every foot jumped costs movement, so you can jump farther than your current speed if you take the Dash action. -Crawford Again.
So, no. Neither the Jump spell nor the Boots of Striding and Springing allow you to exceed your total Speed in distance jumped, though taking the Dash action allows you to move your full Speed a second time during the turn, effectively increasing your Speed by 2x for the round. This lets you actually get some use out of your massively boosted jumping distance. This would rather plainly imply that the Boots of Striding and Springing are generally superior to a Ring of Jumping.
Where this is not true is when you start combining magic items. For example, if you get your hands on a pair of Boots of Speed. Naturally, you can't wear two pairs of boots...but you can wear a pair of boots and a ring. This combination takes two bonus actions to fire up, but then you have a full minute of doubled running speed and tripled jumping distance, without having to take the Dash Action. And because you can get 10 minutes of boosted speed from the boots per day, you can do this 10 times a day. So you have all the mobility of someone Dashing around in Boots of Striding and Springing, but still have your Action free to use.
So, taken in isolation, it does appear that the Boots of Striding and Springing are generally superior to a Ring of Jumping. However, you have 10 fingers for ring-wearing, but can only wear one pair of boots. So the ring is better for combination work.