We have had a wet basement, we are looking for a permanent solution for this. We have been told about digging around the exterior of the house down to the footings to lay drainage tile. The other option we have been informed of is installation of drainage tile inside the foundation. Which is a better option? Both contractors say that their way is the best.
I suggest that you take on this problem one step at a time. Begin by making sure that your gutters are working properly. Do they catch every drop of water that runs off your roof? Do they run to downspouts that direct every drop of that water far away from the house? (And I don't mean splash blocks. The water should run, at bare minimum, 10' away from the house. 20' is better.) If they don't, fix them.
Next, is the soil around your house sloping the right way. It should slope *away* from the house. If it doesn't, think about re-landscaping the yard so that it does. Now, don't just add some barkdust to make it look like it slopes away, I'm talking about the hard layer of earth that's beneath the topsoil. If your yard doesn't slope away from the house, you'll be fighting an uphil battle (so to speak) to get rid of the water.
If you still have a problem after those two issues are addressed, then is the time to think about installing an underground drainage system. If they're done properly, exterior and interior systems work equally well. The decision about where to put the drainage usually boils down to cost. If you have a completely finished basement with lots of partition walls, It can be very expensive to put the drainage there. On the other hand, if your exterior landscaping is complicated, with lots of big trees, retaining walls and expensive plants near the house, exterior drainage work might be more expensive.
A really good drainage contractor should be able to consider the particular conditions of your house and yard and recommend the best course of action. Look for someone with lots of experience and good references that go back several years.