Computational power difference between all interconnected qubit vs few interconnected qubit
A linear chain of qubits has two big disadvantages over a planar grid of qubits:

1) Resilience. If you arrange your qubits into a line, and any one of them doesn't work well, your quantum computer has been cut in half. In a grid you instead end up with a hole that, while inconvenient, can be routed around.

2) Closeness. In a linear chain, the qubits are on average farther apart. So if you want to interact two states, it may take longer to swap them towards each other so that they can interact. That being said, in highly parallel algorithms where you're already saturating all the connections with operations, you tend to be able to combine the swaps with the interactions you wanted to do anyways for no extra cost (e.g. see the paper "Quantum Simulation of Electronic Structure with Linear Depth and Connectivity").