The obvious difference is that you pass a shape into t.new_ones but not into torch.ones_like.
If I remember correctly, the torch.ones_like is an equivalent of the numpy API and t.new_ones is a “torch-legacy-idiomatic” replacement of a long-deprecated t.new method (which incidentally still seems to exist e.g. here pytorch/torch/nn/init.py at b199e3c8427a9648b9a76830ed9898ab4603288c · pytorch/pytorch · GitHub ) which is of similar nature as the deprecated  Tensor(...) and FloatTensor(...) constructors.
Of course, part of the attraction of t.new_ones is that in contrast to C++ with t.options(), you have the “tensor properties” spread over several keyword arguments in Python (dtype, device, memory layout, …), but I tend to prefer torch.ones and torch.ones_like over the t.new_ones.
Best regards
Thomas