Hostel vs Bed and Breakfast

Could you maybe give us an idea of what country you are talking about? Hostels will most likely be cheaper than B&Bs, but you really have to do the math yourself. There is no single answer. It depends on where and when and what is available in the places you want to visit.

I'm going to Amsterdam, Germany, Austria, Italy, and France.

Travelling alone a bed in a collective dorm in a hostel will be all but certainly cheaper than a B&B. However, sleeping in a hostel dorm is not something I'd recommend for people past college age. Some hostels have private rooms with shared bathrooms (or ensuite bathrooms). The overall cost of these rooms is usually akin to what you might find in a much more comfortable hotel if you are willing to trade location for comfort. The second cheapest option for couples or duos is usually a basic room in a basic budget chain like Ibis, Etap, Travelodge etc.

Allie, When people recommend bed and breakfasts, they usually do so because of the charm or coziness, or because they want to "be closer to the locals" (meaning they'll interact with the owners, not a hired hotel clerk). You may find some deals here and there, but generally speaking a B&B isn't a "cheapest option" scenario. As the previous answer said, hostels or discount hotel chains will probably offer better rates. (But lesser quality breakfasts!) You might want to edit your other question (recommendations for particular places) to indicate how much per night you're able to pay rather than just ask about any B&Bs AND hostels. You'll get more hits that way.
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Allie, A bed in a shared room at a hostel will cost between $20 and $35 depending upon the location. A B&B will have a limited number of single rooms or none at all, and they will cost almost as much as a double. The prices vary wildly but maybe between $50 and $80 might be a reasonable guess. If you are not into sharing sleeping areas with others, your inexpensive options are limited, unless you focus on small town lodgings far from the typical tourist routes. There are bargains to be had in locations like that. Have a great trip!

You might want to go to the "Graffiti Wall > Sleeping" column elsewhere on this web site for several topics/discussions that just might help answer your question.

In my last three trips to Germany/Austria, I have spent between €20-€30 per night, EZ U/F, in B&Bs. In all, for SFOPs I have averaged under €32 per night.

Allie, you can get a sense of prices for hostels if you go to a website like Hostelworld.com and plug in your anticipated dates and locations. You can also read review there and see what others have to say about location, safety, cleanliness, noise levels and amenities offered. Some hostels are totally fine, even if you are beyond college, and others are like frat houses. Read the reviews before booking and if you tend to see a pattern of complaints about it being noisy or comments about a late night bar downstairs, you may want to think twice if that doesn't appeal to you. Once you get some prices you can compare them to a B&B or budget hotel. But generally speaking if you are going solo, the bed in a shared dorm at a hostel will be the cheapest unless you wanted to look into the Couchsurfing network.

Allie, Are you travelling "solo"? Dorm rooms in a Hostel will definitely be cheaper than a Bed & Breakfast, but of course one has to be able to tolerate the "group living" environment. Most Hostels have a selektion of rooms from four or six bed Dorms or some with more Beds. Generally speaking, the price decreases inversely with the number of Beds, so a 12-Bed Dorm will be cheaper than a 4-Bed Dorm. Many Hostels these days also offer double rooms, but they tend to be similar in cost to a B&B. All Hostels I've stayed in have included a breakfast of some fashion, so they're somewhat like a B&B. I often "mix" my accommodations when travelling, staying in both Hostels and budget B&B Hotels. Some nights I like to have a bit of privacy. You might find it helpful to have a look at th HI Hostels website, as they likely have properties in all of the towns you'll be visiting. I've found that there facilities tend to be somewhat consistent from one city to the next, and they're well run (NOT party Hostels). Purchase of an inexpensive Membership provides cheaper rates and preffered booking, and the membership is compulsory in some locations. Happy travels!

@Andre L, "However, sleeping in a hostel dorm is not something I'd recommend for people past college age." I'm 60+ so well past College age and I don't have the least problem staying in Dorm rooms in Hostels. I typically choose a four or six bed Dorm, although I've also stayed in some that had about 12 beds. One six bed Dorm that I stayed in was co-ed, and I there didn't seem to be a problem with both males and females in the same room (although I've heard a few stories from other Hostel guests, but I won't elaborate on that). I often find a fairly wide age group staying in Hostels, including some older than me. I try to be considerate (ie: not making a lot of noise when people are trying to sleep), and other guests seem to behave the same way. Cheers!