Shortly after Virgin Trains East Coast announced that they'd be switching to Nectar when their franchise started British Airways had an announcement of their own. Passengers purchasing the cheapest economy tickets would now earn fewer Avios points (Avios is what BA calls their miles) when they travelled. In short: Avios still represent much better value than Nectar points, but the scheme has seen a significant devaluation if you buy the cheapest economy tickets. The cheapest redemption is 9000 Avios for a short haul return + £35 to cover taxes, fees and airport charges (the 9000 Avios rate covers what they call 'Zone 1 Europe' which includes the UK domestic flights, Ireland, France, The Netherlands, Germany, Czech Republic, Switzerland and other flights of similar distance). The minimum you'd earn on a single flight was 500 Avios (this was higher for longer flights over 500 miles or flown in a higher class) meaning you'd earn 1000 Avios for a return flight. So if you were flying between London and Scotland you'd need 9 return trips to get a reward.
The changes to the Avios scheme mean that you now have to take into account your fare type. Most of the cheaper (i.e. not fully-flexible) tickets you'll encounter now earn a minimum of 250 Avios but the lowest fares will now earn a minimum of 125. You're most likely to encounter the 125 point fares if you book far ahead, the average fare paid by most will earn 250. So it would now take 18 return flights to earn the 9000 Avios for a rewards flight if you're travelling on fares that earn 250 Avios and 36 return flights if you're lucky enough to always bag the cheapest fares.
Avios v Nectar
For simplicity let's say your average spend on East Coast is £100 for a standard class return trip. With East Coast Rewards scheme you'd need 255 points for a standard single so it's 510 points for a return. 6 return trips would have got you enough points to cover the 510 points needed. This makes the East Coast Rewards scheme better than the BA Avios scheme. Unfortunately the switch to Nectar means you only get a 1% return so you'd need to make 100 trips to redeem on a ticket of the same value. This means that despite the significant devaluation of the BA scheme it is still significantly more generous than Nectar.
British Airways had a good opportunity to win over some customers from Virgin Trains East Coast. With the new devaluations in the BA scheme I don't think it's worth switching just for the loyalty scheme although it's worth remembering that if you prefer to fly then the BA scheme is still significantly more attractive than Nectar. For regular flyers that don't travel in the premium classes (note that BA domestic is only economy class) or buy pricey fully flexible tickets BA's scheme has turned from good to poor. However the change from East Coast into Virgin Trains East Coast means a switch from excellent to the resulting Nectar scheme which is extremely poor. East Coast Rewards scheme was definitely the best rewards scheme around for domestic travellers by far.
If you do decide to fly BA you can earn Avios by signing up for the BA Executive Club on ba.com or the Avios scheme on avios.com. I recommend using the BA Executive Club route if you're a regular flyer on British Airways as the BA Executive Club also gives you the potential to earn status benefits such as priority boarding and lounge access.
I've simplified things significantly here just looking at the scheme from the point of someone who is only looking at flying to replace their East Coast travel. It's worth reading sites dedicated to Frequent Flyer schemes such as Head for Points if you want to maximise the benefits of the scheme. There are also ways to build up your Avios balance more quickly such as signing up for the British Airways credit card and converting Tesco Clubcard points. Again these options are beyond the scope of this site.