First off some math to compare the two:
Healing spring heal (pet/you) 4.9k + regen 2.3k = 7.2k (the regen heals friendlies too)
An important thing to remember is that you can use blast and leap finishers in HS to heal more.
Water spirit heal (pet/you) 3.8k + .7(traited)*805 per hit = 4.3K if you hit one time traited and 4.1k untraited
If you want to make the comparison fair you have to do attacks/second * 10s(HS uptime) * 805 * % (since you don't want to use the active)
=> SB = 2 APS, SW = 1.7APS, GS = 1.2 APS, LB = 1APS, Ax = 1APS
Traited => SB = 0.7*20*805 = 11.3K, SW = 9.6k, GS = 6.8k, LB/Axe = 5.6K
Untraited => SB = 0.35*20*805 = 5.6K, SW = 4.8k, GS = 3.4k, LB/Axe = 2.8K
It's obvious that not using the traited version is a bad idea since all weapons heal for less than just using HS.
For weapons it's the same thing, if you're not using SB/SW it's simply not worth it.
It greatly depends on what content you're doing and how you're doing it, in most scenarios healing spring>spirit, the exception is dungeon groups where people play in melee (most of the time).
Open World Content:
Let's say you're just leveling, completing hearts,... Chances are high you'll get conditions and need a cleanse, you have several ways of doing this some more costly than others (trait, signet, pet, healing spring, racial (human)) the best pick is clearly HS since you don't really sacrifice anything.
Furthermore your spirit(s) will not avoid AoE damage since the 5target limit of AoE doesn't count = no spirit, no heals
WvW
Again the strength is the condition removal, you can stand in HS and just keep cleansing for 10s (this works nearly as well as the stance from warriors to keep conditions off)
Dungeons
This is where things change, DPS matters, if you really need condition removal you pop on HS but most guards can deal with conditions (and you probably have a guard with you) or a mes with null field. So the basic strong point from the other two aspects is totally negated. As for pure healing output it's obvious that Water Spirit is better for the party since the healing from HS is only regen (2.3k) which gets beaten by all weapons. Add to this that Water Spirit makes it so your party doesn't need to use their heal skill and can just keep attacking (greatly increasing DPS) and you see the clear favorite.
(again some simple math, if everyone aside from you does 10K DPS and a heal skill takes 1s to cast you increase party DPS by 40k!)
TLDR: It depends
1. Traited spirit => good
2. Using SB/SW => good
3. Dungeons => good