It would depend on how you feel afterwords. I would advise that you may want to see about getting the day off if possible. Just so that you can not have to worry if you do not feel 100%.
Normally a dentist does a deep cleaning because you have periodontal disease or otherwise know as gingivitis. You can have bone loss when you have untreated gingivitis. So really the difference in the opinions where not that you do have some degree of periodontal disease/gingivitis but about weather you need fillings or root canal. I think getting the other opinion is a good idea. I do not think anyone is trying to scary you into having work done. Remember that dentist are going to advise what they feel you need. Possible that in your case they each feel that they can correct a problem differently.
That is why in the end you make the decision that you feel is best for you and what you can afford to do.
I hope I have help