I think the reality of it is that a similar thing will happen as did with 3G uptake, the original adaptors got the speeds expected, and then the later adaptors came along, and everyone got slower speeds.
Home broadband has an average contention ratio of 20:1 on copper, meaning that at any one time, you could be sharing the data tunnel to the exchange with 20 other people, so the reality of the situation is that if every one of those 20 went online to stream video, you would get a real world speed of a 20th of that pipe. This was due to the limitations of the copper, but now that we have the Fibre, it is a different story, or at least the figures do not look so bad. At the moment, I believe the contention ratio is 1:1, such that you get your own dedicated space in the fibre back to the exchange, a more guaranteed speed if you will. This is all to do with multiplexing the light streams down the glass fibre, and the fact that you could have thousands of these, each carrying hundreds (if not in the future with new vector multiplexing techniques, thousands) of people's data at very high data rates, where the limitation has yet to be reached.
We now come to 3G (HSDPA, HSUPA) data connections. To keep with the same principles as above, you could be sharing your connection with hundreds of people, such that the contention ratio could be as bad as 2000:1, but the real word differs from this as this is based on the maximum a cell site can handle. You therefore are sharing the data rate between alot more people, so the only way you can get the full speed is to be in a good signal path with a good signal to noise ratio to the tower, and for you to be the only one on it. Due to the equipment and technology, you still have a much bigger latency using a 3G, so that if you were having a live stream sent to your phone, you may notice delays and missing packets. The Skype calls you make may contain hundreds of packets a minute that fail to be received, but you would not notice this as these packets are kept small. Unlike a file transfer, the voice over IP lost packets are not resent, as humans can not pick up these missing packets. However for file transfers, and other times you need a 1-for-1 copy of the original, the latency and mobile phone signal would mean transfer rates are slower that the same 'speed' of a home broadband connection. Also, every time the mobile signal strength changes, the modulation and even technology (3G > EDGE) method changes, so there is packet loss when it changes back and forth.
4G on the other hand has much more advanced technology to deal with all this, and so holds up better, and the speeds will stay higher, but you will never be able to escape the latency, or the speeds jumping around.
In my opinion, and that is only in my opinion, 4G can never replace home internet for people that have good reliable speeds at present with their ADSL connections. It will fulfil the need in the areas that cannot be covered by land based internet communication methods; it would just not be as good as it would be if they had the same 'speed' over copper or fibre.