Which would you recommend: implant or a crown with a post? (Photo)

An X-ray would be very helpful. it is always best to keep your own tooth for as long as possible.  If your dentist thinks that he can restore the tooth with post/ core and crown, then it is a good option A dental implant could always be an option in the future when the time comes that this tooth is not good anymore Remember, dental implants could get problematic as well. 

Hi:At this point if you can get a post and a crown I would recommend this option over an implant.  Best,Dr. Maddahi

If the fracture extends below the bone, Your option is to place the implant, doing the extraction and immediate placement of the implant and a temporary crown.
If the fracture does not extend then place the post / crown is a more conservative option because of your age.
In both scenarios you should take the same care when biting, avoiding or not levering, such as when biting an apple.
Both scenarios have similar behavior and care.
As for the neighboring tooth you also have the option of a veener.
I hope these suggestions help you.

I think it would be good to get a dental implant treatment because its a strong and permanent solution to fix the issue.

 There are pros and cons to each approach… If you do a post and core with a crown you'll keep the natural root and will avoid surgery. If you choose an implant you will not have to worry that the tooth may decay later down the road but replacing the front tooth can be tricky...
If the front tooth bone or root is compromised than an implant can be a better solution. If not,  The more conservative post and core with a crown will often times be very predictable. 
 I agree with your dentist that working on both front teeth (if not the front four) would give you the best final result.