According to what I could find, the Fireheart Skullcap of the Owl has +25 Intellect and +25 Spirit while the Shadowbrim Travel Hat has +19 Stamina +19 Intellect and +12 Spirit. Based on this, I would say the Fireheart Skullcap is considerably better.
It all depends on how you weight the stats. As a Holy Priest, the factors you care about most are how much you can heal, and how long you can heal. IOW, what matters are Healing per Second (HPS), Healing per Mana (HPM) and Mana (through regen and initial pool). As such, the stats you care about are +Healing (HPS, HPM), Spirit (HPS, HPM, Mana), MP5 (Mana), and Intellect (Mana), Spell Haste (HPS).
Of course, Stamina is important too, but only up until you reach a certain amount. For instance, when I'm raid buffed, I like to have over 8000 Health. I can take several 2k hits, and a couple 4k hits. If I had less, I'd get two-shot by 4k hits. In order to survive another 2k hit, I'd need to stack a LOT more stamina, which means I lose out on other valuable stats. In general, you get enough Stamina on gear you get anyway, so I pretty much ignore it (though I still put some value on it in my spreadsheet, so it's not forgotten).
Anyway, back to the relevant stats, +Healing is your base stat, because it allows the most flexibility. It directly affects both HPS and HPM, but for specific fights, if you find you're lacking one compared to the other, you can always adjust the rank of the heal you're using down to increase HPM and up to increase HPS. Spirit is probably the best bang for the buck, point for point, because it affects everything, but affects regen the most, so if you stack spirit heavy, you'll probably want to uprank. MP5, while great for regen, is expensive in terms of itemization, so while it's still desirable, with the buff to spirit, I'd always favor spirit over MP5. Intellect effects your initial pool a lot, and your regen a little, so Intellect is always good, but it's amazing in short fights, and rather lackluster in long ones. Haste is good, but it's, again, situationally useful because you generally have to sacrifice regen to get it, so you not only lose regen, but you burn your mana faster.
That all said, the reason the one item is better is because it has more of the more relevant stats (Intellect and Spirit). It's even easier, because both have the exact same number of total stat points (19+19+12=25+25). So, it really becomes, is it worth trading 6 Stamina for 6 Intellect... generally, yes. Is it worth trading 13 points of Stamina for 13 points of Spirit, almost always, yes.
Of course, keep in mind that all of this analysis is with the assumption that, as a Holy Priest, you have Spiritual Guidance (increases healing and damage by 25% of your spirit) and Meditation. If you don't, the value of Spirit drops considerably. It's also very nice for spirit if you have Improved Divine Spirit (or will get the buff) and have Spirit of Redemption.