I have a severe to profound loss in both ears. I've always worn the full shell ITE aids. I like the convenience of not having the electronics hanging on my ear. Could I get better hearing or power by going with a BTE?

Without consulting in person by examining your test results, discussing your preferences or seeing your ear canal, the most likely answer to your question is yes.  Behind-the-ear hearing aids have more power because of the amplifier size but because the microphones are separated farther from the receiver/output, you can likely achieve higher gain without as much risk of feedback.  In addition, with the components behind your ear there may be more room for additional accessories such as Blue-tooth antenna, etc...Behind the ear technology often has better durability because the internal components aren't as directly subjected to the harsh conditions of the ear canal like an In-the-ear device.  

There is a chance that you could receive more power before the aids start to feed back.  In terms of better hearing, ITEs are generally as good as BTEs from a sound quality standpoint.  It just moves the microphone further away from the receiver to prevent them from feeding back.  Due to this, you could potentially get more power from BTEs.  Without knowing specifics of your current hearing aid capabilities and physical fit of those aids, the answer to your question is impossible to answer exactly.

My preference for most every patient is a BTE w/ a receiver in the canal. However, some patients that have used an ITE previously experience a difference in sound they do not like or don't adjust to. Typically, they are hearing better with the BTE but accepting that new and better sound is a struggle for them. As previously stated in other responses, we can indeed get more power with less squeal using a BTE. For a loss that you describe I would prefer a BTE with a deep seated High Power RIC in a molded earpiece. This arrangement allows maximum power and allows you the many technological advances in today's products. Bluetooth streaming from phone or TV, rechargabilty and directional enhancement are things typically not found in most ITE units. Having a severe loss myself, I've tried about every aid and configuration available and I always come back to the BTE/RIC combination. Personal preference is always a factor in a user's adaptation but in my opinion, better hearing, understanding, and the technology advances outweigh preference when it comes to hearing performance and overall fitting success. 

I would say yes!  I generally recommend BTEs for my patients, either traditional BTEs or RICs.  There are several advantages of the "BTEs" over the ITEs.  BTEs in general have more power before feedback, as much as 10dBs, or 2 times louder.  Also the larger separation of the microphones allows the BTEs to make more decisions within a fix time frame, therefore provide better noise cancellation and other features on the hearing aids.  Lately manufacturers added features such as pina effect, better irrationality features to compensate for the fact that the instrument is worn behind the ears.  You should try them out.  Most outlets allow you to wear them for 30 to 45 days prior to making the decision to purchase.  Just check around.  Good luck

With most manufacturers you will get more power with a behind the ear product as the first reply explains, however, Starkey Hearing Technologies is one manufacturer that always surprises us when it comes to power in a custom product.