Air Travel through Heathrow or Dublin?

You would not go through Immigration while transiting at London Heathrow. You would go through security again.
Dublin has preclearance for US flights and you do go through Immigration there. I am unsure how much extra time this adds to the process and how it might impact the time needed for a connection. Hopefully, someone who has done this will share his/her experience.

I think what I would want to know is how many other flight options are there for my route if I do miss the connection. Which airport would provide more back up options?

Some friends returned to the U.S. two weeks ago after visiting London and Heathrow was the airport they departed from. It took them five hours to get through the gauntlet of lines at Heathrow before they were able to board their plane. In addition to the extended delays at Heathrow, there now is the imminent possibility that British Airways pilots may soon go on strike after they voted this weekend on whether to authorize a strike as a result of stalled contract negotiations. That is something I would not want to get caught up in if there was an alternative airline to fly with.
Dublin is a much smaller airport and the time required to get through security lines last week was just 15 minutes. Pre-clearance for US Citizens returning to the U.S. via Dublin is reportedly taking most passengers 20-40 minutes. For most Global Entry members it is taking 15 minutes.

I would opt for transiting through Dublin.

Having transited both airports quite a few times my first choice would be Dublin. However, I’ve had no issues at either airport. My trips on both airlines have been great. I did not check any bags.

Dublin Airport has not been without its own problems this year, although things have improved somewhat since the spring. Security delays are down to a max of around 45 minutes for example. Bags going missing is maybe the biggest on going problem; there is a mountain of a few thousand stacked up in the midst of processing, mostly from connecting flights. This isn't necessarily down to Dublin airport but the airline or departure airport.

Just today, in a sign of continuing troubles at British Airway's base-- London's Heathrow Airport-- the airline announced it has suspended ticket sales for all short-haul flights out of Heathrow until at least August 8.