I have a background in developing consumer GPS systems...... There is no doubt that a Garmin is a much better device for the job. On cell phones, GPS and associated functionality is the side dish - as in "would you like fries with your burger", on a Garmin, is the Raison d'être.
Hardware wise, its a no brainier.
First, as already mentioned in @armb answer, is battery life - Cell phones start small with the smallest battery they can get away with, ever seen a Cellphone with battery life specified - with GPS turned on - there is a reason for that.
Robustness - cell phone - robust not... There are few slightly rugged ones (I have a Motorola Defy) - but they don't match a Garmin. My defy is supposed to be water proof (IP66, 1/2 hour 1 meter under water). I don't worry about rain, but sure as anything ain't going to put it under water - it has one tiny O ring to seal it, I bet an IP66 Garmin has 2 decent sized ones.
Another issue to think about is that phones have tiny GPS antennas (Remember the fries). Cell phones use assisted start - where the cell network provide key information on start up, allowing them to find the satellites easier. Its easy for a GPS to track where you are once it knows where (and when) you are. If it doesn't know where you are, it doesn't know where to "look" for the satellites, and needs to search for them. Think of looking for a buoy on the water. If you get told, "Find the buoy" it can take forever to find it. With training and binoculars, it's easier, but if I say "The buoy is over there, keep watching it" - anyone can see it (that assisted start).
With no data connection, no assisted start - think minutes to get a fix every time you turn it on, even in perfect conditions, and never in marginal conditions vs Garmin taking a few seconds and nearly always. Research "GPS TTFF" (Time to First Fix). A Garmin with its better GPS front end, will hold the fix much more reliably, if you ride "urban canyons", forests and such like its important.
I mostly use my Defy when on the bike these days - there is a range of Android software probably as good as Garmin has, but you need to find the right one from the hundreds of most rubbish available, install it, jump though hoops with your right pinky finger in you left ear...... Garmin will work out the box.
Sim Card - most cells need a sim card to get past the startup screen.......
Summary - a Cell phone will probably work - with a bit of shagging around, you might even find it acceptable. Garmin will work out the box....