To start with I need to disclose I own an Epson 7880 wide format printer and in my opinion the quality is as good as it gets. Epson inks and premium lustre paper makes for beautiful prints. And with the ability to 24" wide and as long as I want gives me incredible versatility. A little knowledge about color gamuts and properly calibrating monitor to printer is something one must learn to go the home route successfully but well worth it in the final result.
On the other hand I have also used online printing labs for a great deal of my images. In my experience you really need to be careful when choosing your printer. Understand the color model they use and paper stock. I have had some disastrous results from big box store labs...often times the color is simply way off and the paper is always very poor quality. I would not expect the prints to last more than a few years without fading. Using a prolab like White House Custom Prints, Bay Photo Lab or MPIX pro will generally give you superb results but you still need to be wary and thoroughly check the quality when you receive them.
Many people automatically think printing at home is less expensive, this is not the case in my experience. With ink cartridges running as high as $100 each and eight cartridges required the ink costs alone are quite considerable. Rolls of premium paper will cost $150 each and other issues with printers are always a possibility. So before you go out and get yourself a high end printer to save yourself some money, think twice.
For what I do I prefer to print at home as I generally will be printing a large format up to 24x36 and framing them myself. So having the ability to go out and shoot the images, process them and mat and frame all in one day is a huge benefit to me. I once shot a Bride & Groom's portraits in the afternoon, hurried home to print and frame a large 18x24 print of them and then having it displayed near the receiving area at their reception that evening! It made a good impression to say the least :)
In the past when I did school portrait photography and had thousands of prints needed in various sizes in a hurry I used an online lab. This was the only way to practically do this an the results were very acceptable.
Another type of printing I use online labs for is Art Cards, These are very difficult to print on any home printing set-up and the quality from the lab I use is outstanding. If you are ever looking to get some Art Cards printed I highly recommend Art Ink Print in Victoria, BC.