The Shuttle is located at poor locations for transfers to the numbered lines at both ends but is much shallower depth wise. This has to do with the history of the line, and results in a long but flat walk in Grand Central and a connection to the 2/3 requiring differences in elevation.
The 7's elevators at Grand Central are out of service as of December 2019 so getting down means escalators, which may be acceptable for your use case. The connection to the 2/3 is not particularly bad since there is a quick transfer at the eastern end of the 7 train platform at Times Square.
If you're carrying large bulky luggage, the shuttle might be the better option but it is set for heavy renovations and there are guaranteed stairs at Times Square. In contrast, the 7 has step free access at Times Square but requires long escalator rides down to the platform at Grand Central.
I personally feel that the shuttle may be the easiest method, but I'm not a regular user of the shuttle so I'm not as familiar with it.
Edit: As Michael Hampton noted, the shuttle is incredibly packed during rush hours. If you're traveling during AM or PM rush hour the 7 is almost certainly going to be the better option. Do note that if traveling during 4-6 PM on a weekday, getting a 2/3 uptown will be a miserable experience regardless though, in which case avoiding midtown entirely would be recommended if possible.