Personally, I prefer using a computer, especially when going through highly theoretical openings, because often a small difference between two positions result in a different consensus for the preferred treatment. As such, you'd not only want to be able to quickly transition between these positions in order to compare them, but you'll also want an engine that could often tell you why one move works in one position but fails in a similar one.
Here's an example:
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Be3 Bg7 7.f3 O-O 8.Qd2 Nc6 9.O-O-O d5 10.exd5 Nxd5 11.Nxc6 bxc6 12.Nxd5 cxd5 13.Qxd5 Qc7 14.Qxa8 Bf5 15.Qxf8+ Kxf8
is generally regarded as good for black, whereas
1.e4 c5 2.Nf3 d6 3.d4 cxd4 4.Nxd4 Nf6 5.Nc3 g6 6.Be3 Bg7 7.Be2 O-O 8.Qd2 Nc6 9.O-O-O d5 10.exd5 Nxd5 11.Nxc6 bxc6 12.Nxd5 cxd5 13.Qxd5 Qc7 14.Qxa8 Bf5 15.Qxf8+ Kxf8
is preferred for white.
You could of course look at this over the board (in this case, the only difference is a white pawn on f3 and a bishop on c1 versus the pawn remaining on f2 and the bishop on e2) and try to figure out why the evaluations differ, but being told (likely by the engine) that 16.Bd3 runs into 16...Qe5 in only one of these lines isn't going to hurt your absorption of opening knowledge, and saves you the time taken to look for a tactic that is almost part the theory itself.
On the other hand, if you're doing puzzles/tactics, you need to use a board to simulate thinking in a real game (whereas while studying openings, it's more of understanding and memorizing theory that has been developed by others, than trying to find an idea by yourself).
Middlegame-oriented books are somewhat in the middle ground: variations in these books either have a ton of branches (computers let you traverse these quickly), or skip over weak lines whose refutation is not immediately clear to weaker players (the engine gives you an immediate answer). Having said so, it might be better for your development to just take your time with these positions over the board, and try to answer any questions yourself, before asking the engine.
In summary, use computers in cases where you need to move quickly between variations and get insight from the engine, and on the other hand, do things over the board in cases where you need to think for yourself.