Garmin: most models offer 20+ hours of battery life per charge. handhelds have user-replaceable AA batteries. iphones generally have worse battery performance, though some smartphones have beefy batteries, at least as aftermarket accessories. iphones DEFINITELY don't have user-replaceable batteries.
Garmin: accuracy is better than most phones. variability of GPS accuracy varies wildly among phones. the GPS chipset really isn't the component in question (not for newer ones, anyway - for older ones it was), but rather the GPS antenna is the big question mark. most phones use cell towers to augment their craptastic GPS performance due to small antennas. eliminate the cell towers from the equation and you'll see what I'm talking about. that means either go somewhere with no cell reception, or turn off the cellular radio on the phone.
Garmin: more rugged than most phones. you generally have to buy a protective case for a phone to protect it from drops and from moisture and dust. Garmins may be bulkier to start with, but this is generally why they're bulkier. To seal out dust, moisture, and protect the components from shock. a good protective case that handles all of these things for a phone is generally pretty expensive.
Garmin: most touch screen Garmins (aside from the new 600-series Oregons, anyway) use resistive touchscreens, which don't require special gloves to operate like capacitive touchscreens that phones use. This becomes less of an issue as more glove makers make their gloves phone-friendly, but there are still enough gloves out there that are not compatible that it can be an issue if you have special fit issues.
To be fair, phones have faster processors and most apps have better user interfaces than Garmin's. Some of the limitations of phones can be overcome. The GPS accuracy limitation can be overcome by purchasing a bluetooth GPS receiver to pair with your phone. The onboard GPS is really intended for urban wayfinding, and locating a pub or coffeeshop and getting driving directions, rather than accurately recording your path as you bike. A separate GPS receiver will get you that improved accuracy, but it's another battery-powered component and you have to consider its life and the drain on your phone's battery. for phones, there is also not a single app that is as versatile as a Garmin. you have to find an app that does what you want. sometimes you might have to run multiple apps at once, which adds battery drain. and even then, there are some functions that most phone apps just don't do terribly well. namely, loading additional map data. Garmins are limited in that capability in some respects, but the workarounds are very well published. it's not so clear with phones in some cases.
smartphones are expensive. yeah yeah, with your contract you aren't seeing those costs up front. they're amortized in your monthly statement. some people have phone insurance, or the phones are provided by work, or whatever so they don't care. but make no question, you're still paying one way or another. you can spend a lot with a Garmin, also, but that cost is all up front and the Garmin tends to be functional for longer than the phone. and you don't have to worry as much about what happens when you crash or the phone gets wet. if you smash your phone, it's not JUST a GPS. it's your phone, a palm-sized computer with who-knows-what data on it, it's got music, photos, and so on and so forth. is ALL of that stuff backed up somewhere? I hope so. smashing your phone is more headache than smashing a dedicated GPS.
I think if you protect it well and are well aware of the phone's limitations, it's a fine introduction to fitness tracking. But if you start to get more serious about it to the point that you want to start using different sensors, having more accurate data, rely more heavily on it for navigation in remote places, and cleaning up the cockpit of your bike, then a dedicated GPS is your next step. The phone then becomes a backup for you, off, in your pack, in a protective case that keeps it clean and dry and intact. So if you do run into trouble, you can pull it out and use it how you're able. Obviously if you're REALLY out there and there's absolutely no cell reception, its utility will be limited and satellite-based communications (PLB, satellite messengers, sat phones) become more useful.