As someone that's done both, this is my advice. You should pick a brick and mortar store if:
a) You feel that you can either charge a premium and/or increase your volume so dramatically that it will more than pay for the added cost of the store. When I say charge a premium, you usually have to be able to at least DOUBLE your rates and double your number of clients in order to make opening a physical shop worth it.
b) You plan to focus on computer sales vs. just service alone
c) Advertising is difficult in your area and your area typically relies on drive by traffic in order to find products and services. There are a few areas that I know of where it's almost impossible to have a home based business just because online advertising (Adwords, Craigslist, etc.) just doesn't work well. For areas like this, you either have to have a shop, or be willing to barely scrape by for months if not years just to get your name out.
d) Certain areas typically view home based businesses as non-professional and can be mistrusting of home based businesses and avoid them at all costs. For areas like this, a shop is an absolute must.
e) Your home isn't suited to a home based business. If your home is in a bad location, is too small, or is dirty or unwelcoming, it's typically best to open a shop instead of trying to wing it out of your home.
You should choose to run a home based business if:
a) You're a one-man operation and plan to stay that way
b) You mainly go out on-site and don't see that many clients at your location
c) Your competition is intense and you need to compete on price in order to get started. Remember that you should do this only as you start out as it can be difficult to fire these cheap wad clients that you attract later down the road.
d) You prefer to work by appointment rather than have normal business hours. There's no purpose in having a shop if you don't allow walk-in's.