In and of themselves, there are very few differences. The main difference is in the metagame, and where, in PvP, people assign each character to go.
Think of it like Pokemon- You're not gonna send in your psychic type against a dark type. Most melee characters have trouble fighting range characters. So they send the range characters to fight each other, and put the melee somewhere else. This is established via the lanes. Range AD goes bot, Range AP goes mid, and then the melee bruisers go top. Now, with LoL, that ineffectiveness isn't nearly as clear as it is in Pokemon, of course, but it does result in this usual set-up.
As far as the physical differences... Mid is the quickest route across the map, so minions get there earlier, and as such the solo mid gains levels faster. Purple top is easier to gank, and blue bot is easier to gank, because the tribushes there are reversed. It's easy for the jungler to cut it and get behind a laner. So, when it comes to which is more important, ganking top or ganking bot, purple probably has the better end of that deal (because the AD carry, bot, is more important in a match than a bruiser, top).
That said, there's the issue of what Erick mentioned. Although that's not actually a substantial factor, because "angle" only applies for people who play with a locked camera. I play unlocked, and I don't mind purple at all. It's just a shift to make, kind of like switching from normal to smart-casting. It's much better in the long run. Fortunately, I learned that way to begin with, so purple has always felt equivalent to me.
Erick, if you're struggling with purple, I suggest learning unlocked.
The only other substantial physical difference is their positioning to buffs. Consideration of this is more for when you get into PvP, but:
A jungler starting blue will be getting, on the blue side, a leash from top, or on purple, a leash from bot (and mid in either case). A jungler starting red will be getting, on the blue side, a leash from bot, or on purple, a leash from top (and again, mid). Keeping this in mind, you can predict at what time your opponents will reach their lane at the start of a game. However this often does not make a substantial difference unless you plan to get early golems, or to ambush.
Secondly, bot has access to dragon. This is the reason that top goes solo instead of bot- you want two people bot to help control dragon throughout the game. If the enemy bot and mid are mia, your bot and mid can easily run up and check it. If you have a duo top instead, then your bot is 1v2 and your dragon fights will be 2v3 (and you will therefore probably lose).
Finally, baron. The second reason bot is the most important lane is because it is the farthest from baron. This is important, because when an inhibitor breaks, the defending team's safest course of action is to push the broken lane so that superminions don't overrun the base. For the aggressing team, breaking an inhibitor spells an ideal time to baron because the defending team now has to choose between controlling baron, or defending their base, which is a lose-lose choice for them. However, if the defending team pushes a broken top or midlane, they will actually still be somewhat close to baron, and can consequently steal it. If the bot lane is broken and being pushed, they will have to run all the way cross the map to get that baron- which isn't likely to happen. So simply, bot carries the greatest weight for the end-game because getting the bot inhib implies a successful baron.