I've done all three, well technically not AirBnB more VRBO(Homeaway) and I've found that there are pro's and con's to all. In the end it's really going to be up to you and what you like on your vacation. Below are some simplistic pros and cons from my point of view.
Hotels
Pros: Loyalty points and rewards. If you join their rewards program you have a higher priority in getting a room on that busy holiday weekend and possibly getting the good view from that suite all the way up on the east side. Also, you know what to expect...sorta. All hotels aren't equal but if you lean toward 4 or 5 stars you "should" receive 4 or 5 star accommodations and amenities such as in room coffee/tea, cable, stealables (see Gina Yashere), robes, daily maid service and a sense of security.
Cons: If you are trying to save money and eat a meal or two in your room, this type of accommodation typically won't allow that to happen. Even with a microwave and mini-fridge your choices will be limited. If you aren't a picky eater then Uncrustables for breakfast every morning and Top Ramen for dinner may be the way to go for you. Yes I know there are restaurants on site but they are going to cost you! Yes, there are some hotels that throw in breakfast. Again 4/5 star vs 2/3 star.
The other con for me is the fact that it's just a room, a square box with a bed, a nightstand and bathroom on the side. I prefer a little more space when traveling. Even though folks say that you won't spend a lot of time in the room...you will. I promise you, you will. At least 9 to 12 hours. You will want to be comfortable.
Hostels
Pros: Cheap living. Seriously in some parts of the world you can pay as little as $5 to $6 a night for a bed. You also have a higher chance/opportunity of making traveling friends if traveling solo. There are thousands of hostels around the world and Hostelworld.com is a great site to start your search at. Read all the reviews, go back months to years. Google for "traveler" pics. Do not rely solely on the ones supplied by the hostel. Heck that's for any place you are planning on spending your hard earned dollars, big or small. Also Hostels may throw in a free breakfast. Free food is never a bad thing.
Cons: That's really all you get is a twin bed in a room full of strangers along with shared bathroom (toilets and showers). Some of the shared spaces aren't separated by gender. And there generally isn't a safe to place your passport or cash, so be cognizant of how you store your stuff and very much aware of where your passport/phone/laptop type stuff are at all times. This should be with any accommodation but especially here.
Extra: You can get a single occupancy room with a private bathroom that of course will cost you more than $5 a night. More like upwards of $25 to $200 a night.I'm to old to share a toilet on purpose and opt for the private bed/bath options and haven't had a bad experience yet! And I've still made friends, just friends I didn't have to hand tissue to. Read all the reviews and rules for the hostel of your choice! Some hostels have age restrictions (30 and under) and others are party hostels catering to young travelers with open bars and music well into the midnight hour, others go in the exact opposite direction.
AirBnB or VRBO(Homeaway)
Disclaimer this is my favorite mode of living when traveling so....
Pros: Local living in an apartment or home.
Cons: Local living in an apartment or home.
Seriously the pro's and cons are relatively the same. Typically AirBnB's or VRBO's are in local neighborhoods and can involve renting an entire apartment/home or a single room in a strangers home or apartment. Prices vary depending on location and what you want. If you want to wake up next door to folks who live in the city/town/country you are visiting then this is the option for you. Be mindful that you won't be offered the same chances to make traveling friends that a hostel offers and you typically won't have the daily maid service that a hotel offers. On the flip side, this is also a great option if you are traveling in a group. Get an entire home and ball out!
For all three, go with the one that meets your needs and budget. Read all the reviews, use googlemaps to see the neighborhood/hotel and be open to trying something different.
What's your favorite mode of living when traveling?
*I didn't mention resorts or cruises because they are both typically all inclusive and not relative to this discussion.*
Kat